├── SGD_tutorial.pdf ├── README.md ├── sgd_demo.py ├── LICENSE └── SGD.py /SGD_tutorial.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CU-UQ/SGD/HEAD/SGD_tutorial.pdf -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # SGD 2 | Implementation of Stochastic Gradient Descent algorithms in Python (GNU GPLv3) 3 | If you find this code useful please cite the article: 4 | ### Topology Optimization under Uncertainty using a Stochastic Gradient-based Approach ### 5 | Subhayan De, Jerrad Hampton, Kurt Maute, and Alireza Doostan (2020) 6 | Structural and Multidisciplinary Optimization, 62(5), 2255-2278. 7 | https://doi.org/10.1007/s00158-020-02599-z 8 | 9 | ### BibTeX entry: ### 10 | @article{de2020topology, 11 | title={Topology optimization under uncertainty using a stochastic gradient-based approach}, 12 | author={De, Subhayan and Hampton, Jerrad and Maute, Kurt and Doostan, Alireza}, 13 | journal={Structural and Multidisciplinary Optimization}, 14 | volume={62}, 15 | number={5}, 16 | pages={2255--2278}, 17 | year={2020}, 18 | publisher={Springer} 19 | } 20 | 21 | Download the SGD module from https://github.com/CU-UQ/SGD. 22 | See the demo https://github.com/CU-UQ/SGD/blob/master/sgd_demo.py for an example of the implementation. 23 | For a description of the algorithms, see De et al (2020) (https://doi.org/10.1007/s00158-020-02599-z) and Ruder (2016) (https://arxiv.org/abs/1609.04747). 24 | Please report any bugs to Subhayan.De@colorado.edu 25 | ### Website: www.subhayande.com 26 | 27 | Required packages: numpy, time 28 | 29 | This module implements: 30 | (i) Stochastic Gradient Descent, 31 | (ii) SGD with Momentum, 32 | (iii) NAG, 33 | (iv) AdaGrad, 34 | (iv) RMSprop, 35 | (vi) Adam, 36 | (vii) Adamax, 37 | (viii) Adadelta, 38 | (ix) Nadam, 39 | (x) SAG, 40 | (xi) minibatch SGD, 41 | (xii) SVRG. 42 | 43 | *NOTE*: Currently, the stopping conditions are maximum number of iteration and 2nd norm of gradient vector is smaller than a tolerance value. Only, time-delay and exponential learning schedules are implemented. 44 | 45 | Download this file and use *import SGD as sgd* to use the algorithms. 46 | See *sgd_demo.py* for an example. 47 | 48 | -------------------------------------------------------------------------------- /sgd_demo.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | """ 4 | ------------------------------------------------------------------------------- 5 | If you find this code useful please cite the article: 6 | Topology Optimization under Uncertainty using a Stochastic Gradient-based Approach 7 | Subhayan De, Jerrad Hampton, Kurt Maute, and Alireza Doostan (2020) 8 | Structural and Multidisciplinary Optimization, 62(5), 2255-2278. https://doi.org/10.1007/s00158-020-02599-z 9 | BibTeX entry: 10 | @article{de2020topology, 11 | title={Topology optimization under uncertainty using a stochastic gradient-based approach}, 12 | author={De, Subhayan and Hampton, Jerrad and Maute, Kurt and Doostan, Alireza}, 13 | journal={Structural and Multidisciplinary Optimization}, 14 | volume={62}, 15 | number={5}, 16 | pages={2255--2278}, 17 | year={2020}, 18 | publisher={Springer} 19 | } 20 | Download the SGD module from https://github.com/CU-UQ/SGD. 21 | See the demo https://github.com/CU-UQ/SGD/blob/master/sgd_demo.py for an example of the implementation. 22 | For a description of the algorithms, see De et al (2020) (https://doi.org/10.1007/s00158-020-02599-z) and Ruder (2016) (https://arxiv.org/abs/1609.04747). 23 | Please report any bugs to Subhayan.De@colorado.edu 24 | Website: www.subhayande.com 25 | ------------------------------------------------------------------------------- 26 | This file uses a linear regression example to show the use of StochasticGradientDescent module. 27 | Available classes: 28 | (1) Stochastic gradient descent 29 | (2) SGD with momentum 30 | (3) Nesterov accelerated SGD 31 | (4) AdaGrad 32 | (5) RMSprop 33 | (6) Adam 34 | (7) Adamax 35 | (8) Adadelta 36 | (9) Nadam 37 | (10) Stochastic average gradient 38 | (11) Mini-batch stochastic gradient descent 39 | (12) SVRG 40 | 41 | Copyright (C) 2019 Subhayan De 42 | 43 | This program is free software: you can redistribute it and/or modify 44 | it under the terms of the GNU General Public License as published by 45 | the Free Software Foundation, either version 3 of the License, or 46 | (at your option) any later version. 47 | 48 | This program is distributed in the hope that it will be useful, 49 | but WITHOUT ANY WARRANTY; without even the implied warranty of 50 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 51 | GNU General Public License for more details. 52 | 53 | You should have received a copy of the GNU General Public License 54 | along with this program. If not, see . 55 | 56 | Created on Mon Jul 9 21:19:43 2018 57 | @author: Subhayan De (email: Subhayan.De@colorado.edu) 58 | """ 59 | # import matplotlib and numpy packages 60 | import matplotlib 61 | import numpy as np 62 | import matplotlib.pyplot as plt 63 | import matplotlib.cm as cm 64 | 65 | # import the algorithm classes from the SGD module 66 | import SGD as sgd 67 | 68 | def main(): 69 | # Generate data 70 | np.random.seed(0) 71 | n = 1000 72 | X = 2.0*np.random.rand(n,1) 73 | 74 | # parameters 75 | w1 = 3.0 76 | w2 = 4.5 77 | # noisy data 78 | y = w1 + w2 * X + np.random.randn(n,1) 79 | 80 | X_b = np.c_[np.ones((n,1)), X] # add 1 to each instance 81 | # save data and x to files to be used later to calculate objectives and gradients 82 | np.savetxt('test1_data.txt',y) 83 | np.savetxt('test1_x.txt',X_b) 84 | 85 | # select the algorithm to run 86 | # acceptable terms: SGD, SGDmomentum, SGDnesterov, AdaGrad, RMSprop, Adam, Adamax, Adadelta, Nadam, minibatchSGD, SAG, SVRG 87 | alg = 'Adam' 88 | 89 | # initial parameter 90 | w10 = 2.0 91 | w20 = 0.5 92 | theta = np.array([w10, w20]) 93 | R = objFun(theta) # initial objective 94 | it = 0 # set iteration counter to 0 95 | maxIt = 2500 # maximum iteration 96 | dR = gradFun(theta) # initial gradient 97 | if alg == 'SGD': 98 | # Stochastic Gradient Descent 99 | eta = 0.0025 # learning rate 100 | opt = sgd.SGD(obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun) # initialize 101 | opt.performIter() # perform iterations 102 | thetaHist = opt.getParamHist() 103 | elif alg == 'SGDmomentum': 104 | # Stochastic Gradient Descent with momentum 105 | eta = 0.001 # learning rate 106 | opt = sgd.SGD(obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun, momentum = 0.9) # initialize 107 | opt.performIter() # perform iterations 108 | thetaHist = opt.getParamHist() 109 | elif alg == 'SGDnesterov': 110 | # Stochastic Gradient Descent with Nesterov momentum 111 | eta = 0.001 # learning rate 112 | opt = sgd.SGD(obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun, momentum = 0.9,nesterov = True) # initialize 113 | opt.performIter() # perform iterations 114 | thetaHist = opt.getParamHist() 115 | elif alg == 'AdaGrad': 116 | # AdaGrad 117 | eta = 0.25 # learning rate 118 | opt = sgd.AdaGrad(gradHist=0.0,obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun) # initialize 119 | opt.performIter() # perform iterations 120 | thetaHist = opt.getParamHist() 121 | elif alg == 'RMSprop': 122 | # RMSprop 123 | eta = 0.9 # learning rate 124 | opt = sgd.RMSprop(gradHist=0.0,rho=0.1,obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun) # initialize 125 | opt.performIter() # perform iterations 126 | thetaHist = opt.getParamHist() 127 | elif alg == 'Adam': 128 | # Adam 129 | eta = 0.025 # learning rate 130 | opt = sgd.Adam(m = 0.0,v = 0.0,beta1 = 0.9,beta2 = 0.999,obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun) # initialize 131 | opt.performIter() # perform iterations 132 | thetaHist = opt.getParamHist() 133 | elif alg == 'Adamax': 134 | # Adamax 135 | eta = 0.025 # learning rate 136 | opt = sgd.Adamax(m = 0.0,u = 0.0,beta1 = 0.9,beta2 = 0.999,obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun) # initialize 137 | opt.performIter() # perform iterations 138 | thetaHist = opt.getParamHist() 139 | elif alg == 'Adadelta': 140 | # Adadelta 141 | eta = 1.0 # learning rate 142 | opt = sgd.Adadelta(gradHist=0.0,updateHist=0.0,rho=0.99,obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun) # initialize 143 | opt.performIter() # perform iterations 144 | thetaHist = opt.getParamHist() 145 | elif alg == 'Nadam': 146 | # Nadam 147 | eta = 0.01# learning rate 148 | opt = sgd.Nadam(m = 0.0,v = 0.0,beta1 = 0.9,beta2 = 0.999,obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=gradFun) # initialize 149 | opt.performIter() # perform iterations 150 | thetaHist = opt.getParamHist() 151 | elif alg == 'minibatchSGD': 152 | # mini batch stochastic gradient descent 153 | eta = 0.025 # learning rate 154 | opt = sgd.minibatchSGD(nSamples = 10,nTotSamples = n,newGrad = 0.0,obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=batchGradFun) # initialize 155 | opt.performIter() # perform iterations 156 | thetaHist = opt.getParamHist() 157 | elif alg == 'SAG': 158 | # stochastic average gradient descent 159 | eta = 0.0025 # learning rate 160 | opt = sgd.SAG(nSamples = 20,nTotSamples= n, obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=batchGradFun) # initialize 161 | opt.performIter() # perform iterations 162 | thetaHist = opt.getParamHist() 163 | elif alg == 'SVRG': 164 | # stochastic variance reduced gradient descent 165 | eta = 0.004 166 | opt = sgd.SVRG(nTotSamples = n, innerIter = 10, outerIter = 200, option = 1,obj = R, grad = dR, eta = eta, param = theta, iter = it, maxiter=maxIt, objFun=objFun, gradFun=batchGradFun) 167 | opt.performOuterIter() 168 | thetaHist = opt.getParamHist() 169 | else: 170 | raise ValueError('No such algorithm is in the module.\n Please use one of the following options:\nSGD, SGDmomentum, SGDnesterov, AdaGrad, RMSprop, Adam, Adamax, Adadelta, Nadam, minibatchSGD, SAG, SVRG') 171 | 172 | 173 | # Plot the results 174 | matplotlib.rcParams['xtick.direction'] = 'out' 175 | matplotlib.rcParams['ytick.direction'] = 'out' 176 | delta = 0.025 177 | w1 = np.arange(-2.0, 10.0, delta) 178 | w2 = np.arange(-2.0, 10.0, delta) 179 | Xx, Yy = np.meshgrid(w1, w2) 180 | nx = np.shape(Xx) 181 | Z = np.zeros(nx) 182 | for i in range(nx[0]): 183 | for j in range(nx[1]): 184 | Z[i,j] = (np.linalg.norm(y - Xx[i,j]-Yy[i,j]*X,2))**2/n 185 | 186 | plt.figure() 187 | levels = np.arange(0, 40, 4) 188 | CS = plt.contour(Xx, Yy, Z, levels,origin='lower', 189 | linewidths=2, 190 | extent=(-2, 10, -2, 10)) 191 | #plt.clabel(CS, inline=1, fontsize=10) 192 | # Thicken the zero contour. 193 | zc = CS.collections[6] 194 | plt.setp(zc, linewidth=4) 195 | 196 | plt.clabel(CS, levels[1::2], # label every second level 197 | inline=1, 198 | fmt='%1.1f', 199 | fontsize=10) 200 | im = plt.imshow(Z, interpolation='bilinear', origin='lower', cmap=cm.Wistia, extent=(-2, 10, -2, 10)) 201 | 202 | # make a colorbar 203 | plt.colorbar(im, shrink=0.8, extend='both') 204 | plt.plot(thetaHist[0,:], thetaHist[1,:],'r.',linewidth = 6) 205 | titl = opt.alg+' with a learning rate '+str(eta) 206 | plt.title(titl) 207 | return opt 208 | 209 | def objFun(param): 210 | # objective function 211 | y = np.loadtxt('test1_data.txt') 212 | X_b = np.loadtxt('test1_x.txt') 213 | n = np.size(y) 214 | yprime = X_b.dot(param) 215 | obj = np.sum(np.multiply(y-yprime,y-yprime))/n 216 | return obj 217 | 218 | def gradFun(param): 219 | # gradient function 220 | y = np.loadtxt('test1_data.txt') 221 | X_b = np.loadtxt('test1_x.txt') 222 | n = np.size(y) 223 | nprime = np.random.randint(n) 224 | xi = X_b[nprime:nprime+1] 225 | yi = y[nprime:nprime+1] 226 | grad = 2.0 * xi.T.dot(xi.dot(param) - yi) 227 | return grad 228 | 229 | def batchGradFun(param,nBatch): 230 | # batch gradient function 231 | y = np.loadtxt('test1_data.txt') 232 | X_b = np.loadtxt('test1_x.txt') 233 | n = np.size(y) 234 | nParam = np.size(param) 235 | batchGrad = np.zeros((nParam,nBatch)) 236 | nprime = np.random.choice(range(n), nBatch, replace = False) 237 | for i in range(nBatch): 238 | xi = X_b[nprime[i]:nprime[i]+1] 239 | yi = y[nprime[i]:nprime[i]+1] 240 | batchGrad[:,i] = 2.0 * xi.T.dot(xi.dot(param) - yi) 241 | return batchGrad,nprime 242 | 243 | if __name__ == "__main__": 244 | opt = main() 245 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /SGD.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | """ 4 | ------------------------------------------------------------------------------- 5 | If you find this code useful please cite the article: 6 | 7 | Topology Optimization under Uncertainty using a Stochastic Gradient-based Approach 8 | Subhayan De, Jerrad Hampton, Kurt Maute, and Alireza Doostan (2020) 9 | Structural and Multidisciplinary Optimization, 62(5), 2255-2278. 10 | https://doi.org/10.1007/s00158-020-02599-z 11 | 12 | BibTeX entry: 13 | @article{de2020topology, 14 | title={Topology optimization under uncertainty using a stochastic gradient-based approach}, 15 | author={De, Subhayan and Hampton, Jerrad and Maute, Kurt and Doostan, Alireza}, 16 | journal={Structural and Multidisciplinary Optimization}, 17 | volume={62}, 18 | number={5}, 19 | pages={2255--2278}, 20 | year={2020}, 21 | publisher={Springer} 22 | } 23 | 24 | Download the SGD module from https://github.com/CU-UQ/SGD. 25 | See the demo https://github.com/CU-UQ/SGD/blob/master/sgd_demo.py for an example of the implementation. 26 | For a description of the algorithms, see De et al (2020) (https://doi.org/10.1007/s00158-020-02599-z) and Ruder (2016) (https://arxiv.org/abs/1609.04747). 27 | Please report any bugs to Subhayan.De@colorado.edu 28 | Website: www.subhayande.com 29 | ------------------------------------------------------------------------------- 30 | 31 | This is the class file that implements: 32 | (i) Stochastic Gradient Descent, 33 | (ii) SGD with Momentum, 34 | (iii) NAG, 35 | (iv) AdaGrad, 36 | (iv) RMSprop, 37 | (vi) Adam, 38 | (vii) Adamax, 39 | (viii) Adadelta, 40 | (ix) Nadam, 41 | (x) SAG, 42 | (xi) minibatch SGD, 43 | (xii) SVRG. 44 | 45 | NOTE: Currently, the stopping conditions are maximum number of iteration and 2nd norm of gradient vector 46 | and time-delay and exponential learnong schedules are implemented. 47 | 48 | Copyright (C) 2019 Subhayan De 49 | 50 | This program is free software: you can redistribute it and/or modify 51 | it under the terms of the GNU General Public License as published by 52 | the Free Software Foundation, either version 3 of the License, or 53 | (at your option) any later version. 54 | 55 | This program is distributed in the hope that it will be useful, 56 | but WITHOUT ANY WARRANTY; without even the implied warranty of 57 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 58 | GNU General Public License for more details. 59 | 60 | You should have received a copy of the GNU General Public License 61 | along with this program. If not, see . 62 | 63 | Created on Sat Jun 30 01:04:28 2018 64 | @author: Subhayan De 65 | 66 | Report any bugs to Subhayan.De@colorado.edu 67 | 68 | Author's note: add kSGD, 2nd order methods 69 | """ 70 | 71 | import numpy as np 72 | import time 73 | 74 | # Print iterations progress 75 | def printProgressBar (iteration, total, prefix = '', suffix = '', decimals = 1, length = 100, fill = '█'): 76 | """ 77 | Call in a loop to create terminal progress bar 78 | parameters: 79 | iteration - Required : current iteration (Int) 80 | total - Required : total iterations (Int) 81 | prefix - Optional : prefix string (Str) 82 | suffix - Optional : suffix string (Str) 83 | decimals - Optional : positive number of decimals in percent complete (Int) 84 | length - Optional : character length of bar (Int) 85 | fill - Optional : bar fill character (Str) 86 | """ 87 | percent = ("{0:." + str(decimals) + "f}").format(100 * (iteration / float(total))) 88 | filledLength = int(length * iteration // total) 89 | bar = fill * filledLength + '-' * (length - filledLength) 90 | print('\r%s |%s| %s%% %s' % (prefix, bar, percent, suffix), end = '\r') 91 | # Print New Line on Complete 92 | if iteration == total: 93 | print() 94 | 95 | 96 | class SGD(object): 97 | """ 98 | ============================================================================== 99 | | Stochastic Gradient Descent class | 100 | ============================================================================== 101 | Initialization: 102 | sgd = SGD(obj, grad, eta, param, iter, maxIter, objFun, gradFun, 103 | lowerBound, upperBound, stopGrad, momentum, nesterov, 104 | learnSched, lrParam) 105 | 106 | NOTE: To perform just one iteration provide either grad or gradFn. 107 | obj or objFn are optional. 108 | ============================================================================== 109 | Attributes: 110 | obj: objective (optional input) 111 | grad: Gradient information 112 | (array of dimension nParam-by-1, optional input) 113 | eta: learning rate ( = 1.0, default) 114 | param: the parameter vector (array of dimension nParam-by-1) 115 | nParam: number of parameters 116 | iter: iteration number 117 | maxIter: maximum iteration number (optional, default = 1) 118 | objFun: function handle to evaluate the objective 119 | (not required for maxit = 1 ) 120 | gradFun: function handle to evaluate the gradient 121 | (not required for maxit = 1 ) 122 | lowerBound: lower bound for the parameters (optional input) 123 | upperBound: upper bound for the parameters (optional input) 124 | paramHist: parameter evolution history 125 | stopGrad: stopping criterion based on 2-norm of gradient vector 126 | momentum: momentum parameter (default = 0) 127 | nesterov: set to True if Nesterov momentum equation to be used 128 | (default = False) 129 | learnSched: learning schedule (constant, exponential or time-based, 130 | default = constant) 131 | lrParam: learning schedule parameter (default =0.1) 132 | alg: algorithm used 133 | __version__:version of the code 134 | ============================================================================== 135 | Methods: 136 | Public: 137 | getParam: returns the parameter values 138 | getObj: returns the current objective value 139 | getGrad: returns the current gradient information 140 | update: perform a single iteration 141 | performIter: perform maxIter number of iterations 142 | getParamHist: returns parameter update history 143 | Private: 144 | __init___: initialization 145 | evaluateObjFn: evaluates the objective function 146 | evaluateGradFn: evaluates the gradients 147 | satisfyBounds: satisfies the parameter bounds 148 | learningSchedule: learning schedule 149 | stopCrit: check stopping criteria 150 | ============================================================================== 151 | Reference: Bottou, Léon, Frank E. Curtis, and Jorge Nocedal. 152 | "Optimization methods for large-scale machine learning." 153 | SIAM Review 60.2 (2018): 223-311. 154 | ============================================================================== 155 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 156 | ============================================================================== 157 | """ 158 | def __init__(self,**kwargs): 159 | allowed_kwargs = {'obj', 'grad', 'param', 'eta', 'iter', 'maxiter', 'objFun', 'gradFun', 'lowerBound', 'upperBound', 'oldGrad', 'stopGrad', 'momentum', 'nesterov','learnSched', 'lrParam'} 160 | for k in kwargs: 161 | if k not in allowed_kwargs: 162 | raise TypeError('Unexpected keyword argument passed to optimizer at: ' + str(k)) 163 | 164 | self.__dict__.update(kwargs) 165 | self.nParam = np.size(self.param) 166 | # Checks and setting default values 167 | # Iteration numbers 168 | if hasattr(self,'iter') == False: 169 | self.iter = 0 # set the iteration number 170 | self.currentIter = self.iter 171 | # stopping criteria 172 | # max iteration no. 173 | if hasattr(self,'maxiter') == False: 174 | self.maxiter = 1 # set the default max iteration number 175 | # minimum gradient 176 | if hasattr(self,'stopGrad') == False: 177 | self.stopGrad = 1e-6 178 | # Parameter values 179 | if hasattr(self,'param') == False: 180 | raise ValueError('Parameter vector is missing') 181 | # Gradient information 182 | if hasattr(self,'grad') == False: 183 | print('No gradient information provided at iteration: 1') 184 | if hasattr(self,'gradFun') == False: 185 | raise ValueError('Please provide the gradient function') 186 | elif np.size(self.grad) != self.nParam: 187 | raise ValueError('Gradient dimension mismatch') 188 | if self.maxiter > 1 and hasattr(self,'gradFun') == False: 189 | raise ValueError('Please provide the gradient function') 190 | # Objective values 191 | if hasattr(self,'objFun') == False and self.maxiter > 1: 192 | raise ValueError('Please provide the objective function') 193 | if hasattr(self,'obj') == False: 194 | self.obj = np.array([]) 195 | if hasattr(self,'objFun'): 196 | self.evaluateObjFn(self) 197 | else: 198 | self.obj = np.array([self.obj]) 199 | # Learning rate 200 | if hasattr(self,'eta') == False: 201 | self.eta = 1.0 202 | print('*NOTE: No learning rate provided, assumed as 1.0') 203 | else: 204 | print('Learning rate = ',self.eta,'\n') 205 | if hasattr(self,'lowerBound') == False: 206 | self.lowerBound = -np.inf*np.ones(self.nParam) 207 | elif np.size(self.lowerBound) == 1: 208 | self.lowerBound = self.lowerBound*np.ones(self.nParam) 209 | else: 210 | raise ValueError('parameter lower bound dimension mismatch') 211 | # Set the upper bounds 212 | if hasattr(self,'upperBound') == False: 213 | self.upperBound = np.inf*np.ones(self.nParam) 214 | elif np.size(self.upperBound) == 1: 215 | self.upperBound = self.upperBound*np.ones(self.nParam) 216 | else: 217 | raise ValueError('parameter upper bound dimension mismatch') 218 | # Momentum 219 | #self.alg = 'SGD with Momentum' 220 | if hasattr(self,'alg') == False: 221 | self.alg = 'SGD+momentum' 222 | if hasattr(self,'momentum') == False: 223 | self.alg = 'SGD' 224 | self.momentum = 0.0; 225 | self.paramHist = np.reshape(self.param,(2,1)) 226 | self.__version__ = '0.0.1' 227 | self.stop = False 228 | self.updateParam = np.zeros(self.nParam) 229 | # Nesterov momentum 230 | if hasattr(self, 'nesterov'): 231 | if self.nesterov == True: 232 | self.alg = 'SGD+Nesterov momentum' 233 | if hasattr(self,'gradFun') == False: 234 | raise ValueError('provide gradient function information with Nesterov') 235 | else: 236 | self.nesterov = False 237 | # learning schedule 238 | if hasattr(self,'learnSched') == False: 239 | self.learnSched = 'constant' 240 | elif self.learnSched != 'exponential' and self.learnSched != 'time-based': 241 | print('no such learning schedule in this module\nSet to constant') 242 | self.learnSched = 'constant' 243 | elif hasattr(self,'lrParam') == False: 244 | self.lrParam = 0.1 245 | print('Learning schedule: ',self.learnSched) 246 | 247 | 248 | def __version__(self): 249 | """ 250 | version of the code 251 | """ 252 | print(self.__version__) 253 | 254 | def getParam(self): 255 | """ 256 | To get the next parameter values 257 | """ 258 | print(self.nParam,'parameters have been updated!\n') 259 | return self.param 260 | 261 | def getObj(self): 262 | """ 263 | To get the current objective (if possible) 264 | """ 265 | self.evaluateObjFn() 266 | return self.obj 267 | 268 | def getGrad(self): 269 | """ 270 | To get the gradients 271 | """ 272 | return self.grad 273 | 274 | def getParamHist(self): 275 | """ 276 | To get parameter history 277 | """ 278 | return self.paramHist 279 | 280 | def evaluateObjFn(self): 281 | """ 282 | This evalutes the objective function 283 | objFun should be a function handle with input: param, output: objective 284 | """ 285 | if not self.obj.any(): 286 | print('No objective information provided to SGD') 287 | else: 288 | self.obj = np.append(self.obj,self.objFun(self.param)) 289 | #print('Current objective value: ', self.obj[self.currentIter],'\n') 290 | 291 | def evaluateGradFn(self): 292 | """ 293 | This evalutes the gradient function for i-th data point, where i in [0, n] 294 | gradFun should be a function handle with input: param, output: gradient 295 | """ 296 | self.grad = self.gradFun(self.param) 297 | 298 | def satisfyBounds(self): 299 | """ 300 | This satisfies the parameter bounds (if any) 301 | """ 302 | # Set the lower bounds 303 | #print(self.lowerBound) 304 | 305 | # Satisfy the bounds 306 | for i in range(self.nParam): 307 | if self.param[i] > self.upperBound[i]: 308 | self.param[i] = self.upperBound[i] 309 | elif self.param[i] < self.lowerBound[i]: 310 | self.param[i] = self.lowerBound[i] 311 | 312 | def update(self): 313 | """ 314 | Perform one iteration of SGD 315 | """ 316 | # Perform one iteration of SGD 317 | SGD.learningSchedule(self) 318 | if self.nesterov == True: 319 | grdnt = self.gradFun(self.param - self.momentum*self.updateParam) 320 | self.updateParam = self.updateParam*self.momentum + self.etaCurrent*grdnt 321 | else: 322 | self.updateParam = self.updateParam*self.momentum + self.etaCurrent*self.grad 323 | self.param=self.param - self.updateParam 324 | #self.param=self.param - self.eta*self.grad 325 | # satisfy the parameter bounds 326 | SGD.satisfyBounds(self) 327 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 328 | #print('One iteration of Stochatsic Gradient Descent has been performed successfully!\n') 329 | 330 | def performIter(self): 331 | """ 332 | Performs all the iterations of SGD 333 | """ 334 | SGD.printAlg(self) 335 | # initialize progress bar 336 | printProgressBar(0, self.maxiter, prefix = self.alg, suffix = 'Complete', length = 25) 337 | self.t = time.clock() 338 | for i in range(self.iter,self.maxiter,1): 339 | if self.stop == True: 340 | break 341 | #print('iteration', i+1, 'out of', self.maxiter) 342 | self.update() 343 | self.currentIter = i+1 344 | # print progress bar 345 | SGD.printProgress(self) 346 | # Update the objective and gradient 347 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 348 | SGD.evaluateObjFn(self) 349 | SGD.evaluateGradFn(self) 350 | SGD.stopCrit(self) 351 | 352 | def stopCrit(self): 353 | """ 354 | Checks stopping criteria 355 | """ 356 | if self.grad.ndim >1: 357 | self.avgGrad = np.mean(self.grad,axis =1) 358 | if np.linalg.norm(self.avgGrad) 1: # since objFun and gradFun are optional for 1 iteration 498 | SGD.evaluateObjFn(self) 499 | SGD.evaluateGradFn(self) 500 | SGD.stopCrit(self) 501 | 502 | def getGradHist(self): 503 | """ 504 | Returns accumulated gradient history 505 | """ 506 | return self.gradHist 507 | 508 | class RMSprop(SGD): 509 | """ 510 | ============================================================================== 511 | | RMSprop class | 512 | | derived class from Stochastic Gradient Descent | 513 | ============================================================================== 514 | Initialization: 515 | rp = RMSprop(gradHist, updatehist, rho, obj, grad, eta, param, 516 | iter, maxIter, objFun, gradFun, lowerBound, upperBound) 517 | NOTE: gradHist: historical information of gradients 518 | (array of dimension nparam-by-1) 519 | this should equal to zero for 1st iteration 520 | ============================================================================== 521 | Attributes: 522 | grad: Gradient information (array of dimension nParam-by-1) 523 | eta: learning rate = 1 by default 524 | param: the parameter vector (array of dimension nParam-by-1) 525 | nParam: number of parameters 526 | gradHist: gradient history accumulator (see the algorithm) 527 | epsilon: square-root of machine-precision 528 | (required to avoid division by zero) 529 | rho: exponential decay rate (0.95 may be a good choice) 530 | iter: iteration number (optional) 531 | maxIter: maximum iteration number (optional input, default = 1) 532 | objFun: function handle to evaluate the objective 533 | (not required for maxit = 1 ) 534 | gradFun: function handle to evaluate the gradient 535 | (not required for maxit = 1 ) 536 | lowerBound: lower bound for the parameters (optional input) 537 | upperBound: upper bound for the parameters (optional input) 538 | stopGrad: stopping criterion based on 2-norm of gradient vector 539 | (default 10^-6) 540 | alg: algorithm used 541 | __version__: version of the code 542 | ============================================================================== 543 | Methods: 544 | Public: 545 | performIter:performs all the iterations inside a for loop 546 | getGradHist:returns gradient history (default is zero) 547 | Inherited: 548 | getParam: returns the parameter values 549 | getObj: returns the current objective value 550 | getGrad: returns the current gradient information 551 | getParamHist: returns parameter update history 552 | Private: (should not be called outside this class file) 553 | __init__: initialization 554 | update: performs one iteration of Adadelta 555 | Inherited: 556 | evaluateObjFn: evaluates the objective function 557 | evaluateGradFn: evaluates the gradients 558 | satisfyBounds: satisfies the parameter bounds 559 | learningSchedule: learning schedule 560 | stopCrit: check stopping criteria 561 | ============================================================================== 562 | Reference: Geoffrey Hinton 563 | "rmsprop: Divide the gradient by a running average of its recent magnitude." 564 | http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf. 565 | ============================================================================== 566 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 567 | ============================================================================== 568 | """ 569 | def __init__(self,gradHist=0.0,rho=0.9,**kwargs): 570 | """ Initialize the Adadelta class object. 571 | This can be used to perform one iteration of Adadelta. 572 | """ 573 | self.alg = 'RMSprop' 574 | SGD.printAlg(self) 575 | SGD.__init__(self,**kwargs) 576 | self.epsilon=np.finfo(float).eps # The machine precision 577 | # Initialize gradient history 578 | if np.sum(gradHist) != 0.0: 579 | if np.size(gradHist) != self.nParam: 580 | raise ValueError('Gradient history dimension mismatch') 581 | else: 582 | self.gradHist=np.reshape(gradHist,(self.nParam)) 583 | else: 584 | self.gradHist = np.zeros(self.nParam) 585 | # Initialize rho 586 | self.rho = rho 587 | 588 | def update(self): 589 | """ 590 | Perform one iteration of RMSprop 591 | """ 592 | # update gradient history acccumulator 593 | SGD.learningSchedule(self) 594 | self.gradHist+=self.rho*self.gradHist+(1.0-self.rho)*np.multiply(self.grad,self.grad); # Sum of gradient history 595 | # Perform one iteration of RMSprop 596 | RMSg = np.sqrt(self.gradHist)+self.epsilon 597 | updateParam = ((np.divide(self.grad,RMSg))) 598 | self.param=self.param-self.etaCurrent*updateParam 599 | SGD.satisfyBounds(self) 600 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 601 | #print('One iteration of RMSprop has been performed successfully!\n') 602 | 603 | def performIter(self): 604 | """ 605 | Performs all the iterations of RMSprop 606 | """ 607 | # initialize progress bar 608 | printProgressBar(0, self.maxiter, prefix = self.alg, suffix = 'Complete', length = 25) 609 | self.t = time.clock() 610 | for i in range(self.iter,self.maxiter,1): 611 | if self.stop == True: 612 | break 613 | #print('iteration', i+1, 'out of', self.maxiter) 614 | self.update() 615 | self.currentIter = i+1 616 | # print progress bar 617 | SGD.printProgress(self) 618 | # Update the objective and gradient 619 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 620 | SGD.evaluateObjFn(self) 621 | SGD.evaluateGradFn(self) 622 | SGD.stopCrit(self) 623 | 624 | def getGradHist(self): 625 | """ 626 | This returns the gradient history 627 | """ 628 | return self.gradHist 629 | 630 | class Adam(SGD): 631 | """ 632 | ============================================================================== 633 | | Adaptive moment estimation (Adam) class | 634 | | derived class from Stochastic Gradient Descent | 635 | ============================================================================== 636 | Initialization: 637 | adm = Adam(m, v, beta1, beta2, obj, grad, eta, param, 638 | iter, maxIter, objFun, gradFun, lowerBound, upperBound) 639 | 640 | ============================================================================== 641 | Attributes: 642 | grad: Gradient information (array of dimension nParam-by-1) 643 | eta: learning rate 644 | param: the parameter vector (array of dimension nParam-by-1) 645 | nParam: number of parameters 646 | beta1, beta2: exponential decay rates in [0,1) 647 | (default beta1 = 0.9, beta2 = 0.999) 648 | m: First moment (array of dimension nParam-by-1) 649 | v: Second raw moment (array of dimension nParam-by-1) 650 | epsilon: square-root of machine-precision 651 | (required to avoid division by zero) 652 | iter: iteration number 653 | maxIter: maximum iteration number (optional input, default = 1) 654 | objFun: function handle to evaluate the objective 655 | (not required for maxit = 1 ) 656 | gradFun: function handle to evaluate the gradient 657 | (not required for maxit = 1 ) 658 | lowerBound: lower bound for the parameters (optional input) 659 | upperBound: upper bound for the parameters (optional input) 660 | stopGrad: stopping criterion based on 2-norm of gradient vector 661 | (default 10^-6) 662 | alg: algorithm used 663 | __version__: version of the code 664 | ============================================================================== 665 | Methods: 666 | Public: 667 | performIter: performs all the iterations inside a for loop 668 | getGradHist: returns gradient history (default is zero) 669 | getMoments: returns history of moments 670 | Inherited: 671 | getParam: returns the parameter values 672 | getObj: returns the current objective value 673 | getGrad: returns the current gradient information 674 | getParamHist: returns parameter update history 675 | Private: (should not be called outside this class file) 676 | __init__: initialization 677 | update: performs one iteration of Adam 678 | Inherited: 679 | evaluateObjFn: evaluates the objective function 680 | evaluateGradFn: evaluates the gradients 681 | satisfyBounds: satisfies the parameter bounds 682 | learningSchedule: learning schedule 683 | stopCrit: check stopping criteria 684 | ============================================================================== 685 | Reference: Kingma, Diederik P., and Jimmy Ba. 686 | "Adam: A method for stochastic optimization." 687 | arXiv preprint arXiv:1412.6980 (2014). 688 | ============================================================================== 689 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 690 | ============================================================================== 691 | """ 692 | def __init__(self,m = 0.0,v = 0.0,beta1 = 0.9,beta2 = 0.99,**kwargs): 693 | # def __init__(self,grad,learningRate,parameters,numParam,gradHist,beta1,beta2): 694 | """ Initialize the adagrad class object. 695 | This can be used to perform one iteration of Adam. 696 | """ 697 | self.alg = 'Adam' 698 | SGD.printAlg(self) 699 | self.beta1 = beta1 # decay rate (beta1 = 0.9 is a good suggestion) 700 | self.beta2 = beta2 # decay rate (beta2 = 0.999 is a good suggetion) 701 | self.epsilon=np.finfo(float).eps # The machine precision 702 | SGD.__init__(self,**kwargs) 703 | # Initialize first moment 704 | if np.sum(m) != 0.0: 705 | if np.size(m) != self.nParam: 706 | raise ValueError('First moment dimension mismatch') 707 | else: 708 | self.m=np.reshape(m,(self.nParam)) 709 | else: 710 | self.m = np.zeros(self.nParam) 711 | # Initialize second raw moment 712 | if np.sum(v) != 0.0: 713 | if np.size(v) != self.nParam: 714 | raise ValueError('Second raw moment dimension mismatch') 715 | else: 716 | self.v=np.reshape(v,(self.nParam)) 717 | else: 718 | self.v = np.zeros(self.nParam) 719 | 720 | def update(self): 721 | """ Perform one iteration of Adam 722 | """ 723 | SGD.learningSchedule(self) 724 | # Moment updates 725 | self.m = self.beta1*self.m + (1.0-self.beta1)*self.grad # Update biased first moment estimate 726 | self.mHat = self.m/(1.0-self.beta1**(self.currentIter+1)) # Compute bias-corrected first moment estimate 727 | #print(self.mHat) 728 | self.v = self.beta2*self.v + (1.0-self.beta2)*np.multiply(self.grad,self.grad) # Update biased second moment estimate 729 | self.vHat = self.v/(1.0-self.beta2**(self.currentIter+1)) # Compute bias-corrected second moment estimate 730 | # Parameter updates 731 | self.param = self.param - np.divide((self.etaCurrent*self.mHat),(np.sqrt(self.vHat))+self.epsilon) 732 | SGD.satisfyBounds(self) 733 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 734 | #print('One iteration of Adam has been performed successfully!\n') 735 | 736 | def performIter(self): 737 | """ 738 | Performs all the iterations of Adam 739 | """ 740 | # initialize progress bar 741 | printProgressBar(0, self.maxiter, prefix = self.alg, suffix = 'Complete', length = 25) 742 | self.t = time.clock() 743 | for i in range(self.iter,self.maxiter,1): 744 | if self.stop == True: 745 | break 746 | #print('iteration', i+1, 'out of', self.maxiter) 747 | self.update() 748 | self.currentIter = i+1 749 | # print progress bar 750 | SGD.printProgress(self) 751 | # Update the objective and gradient 752 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 753 | SGD.evaluateObjFn(self) 754 | SGD.evaluateGradFn(self) 755 | SGD.stopCrit(self) 756 | 757 | def getMoments(self): 758 | """ 759 | This returns the updated moments 760 | """ 761 | return self.m, self.v 762 | 763 | class Adamax(SGD): 764 | """ 765 | ============================================================================== 766 | | Adaptive moment estimation (Adamax) class | 767 | | derived class from Stochastic Gradient Descent | 768 | ============================================================================== 769 | Initialization: 770 | admx = Adamax(m, v, beta1, beta2, obj, grad, eta, param, 771 | iter, maxIter, objFun, gradFun, lowerBound, upperBound) 772 | 773 | ============================================================================== 774 | Attributes: (all private) 775 | grad: Gradient information (array of dimension nParam-by-1) 776 | eta: learning rate 777 | param: the parameter vector (array of dimension nParam-by-1) 778 | nParam: number of parameters 779 | beta1, beta2: exponential decay rates in [0,1) 780 | (default beta1 = 0.9, beta2 = 0.999) 781 | m: First moment (array of dimension nParam-by-1) 782 | u: infinity norm constrained second moment 783 | (array of dimension nParam-by-1) 784 | epsilon: square-root of machine-precision 785 | (required to avoid division by zero) 786 | iter: iteration number 787 | maxIter: maximum iteration number (optional input, default = 1) 788 | objFun: function handle to evaluate the objective 789 | (not required for maxit = 1 ) 790 | gradFun: function handle to evaluate the gradient 791 | (not required for maxit = 1 ) 792 | lowerBound: lower bound for the parameters (optional input) 793 | upperBound: upper bound for the parameters (optional input) 794 | stopGrad: stopping criterion based on 2-norm of gradient vector 795 | (default 10^-6) 796 | alg: algorithm used 797 | __version__: version of the code 798 | ============================================================================== 799 | Methods: 800 | Public: 801 | performIter: performs all the iterations inside a for loop 802 | getGradHist: returns gradient history (default is zero) 803 | getMoments: returns history of moments 804 | Inherited: 805 | getParam: returns the parameter values 806 | getObj: returns the current objective value 807 | getGrad: returns the current gradient information 808 | getParamHist: returns parameter update history 809 | Private: (should not be called outside this class file) 810 | __init__: initialization 811 | update: performs one iteration of Adam 812 | Inherited: 813 | evaluateObjFn: evaluates the objective function 814 | evaluateGradFn: evaluates the gradients 815 | satisfyBounds: satisfies the parameter bounds 816 | learningSchedule: learning schedule 817 | stopCrit: check stopping criteria 818 | ============================================================================== 819 | Reference: Kingma, Diederik P., and Jimmy Ba. 820 | "Adam: A method for stochastic optimization." 821 | arXiv preprint arXiv:1412.6980 (2014). 822 | ============================================================================== 823 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 824 | ============================================================================== 825 | """ 826 | def __init__(self,m = 0.0,u = 0.0,beta1 = 0.9,beta2 = 0.99,**kwargs): 827 | # def __init__(self,grad,learningRate,parameters,numParam,gradHist,beta1,beta2): 828 | """ Initialize the adagrad class object. 829 | This can be used to perform one iteration of Adamax. 830 | """ 831 | self.alg = 'Adamax' 832 | SGD.printAlg(self) 833 | self.beta1 = beta1 # decay rate (beta1 = 0.9 is a good suggestion) 834 | self.beta2 = beta2 # decay rate (beta2 = 0.999 is a good suggetion) 835 | self.epsilon=np.finfo(float).eps # The machine precision 836 | SGD.__init__(self,**kwargs) 837 | # Initialize first moment 838 | if np.sum(m) != 0.0: 839 | if np.size(m) != self.nParam: 840 | raise ValueError('First moment dimension mismatch') 841 | else: 842 | self.m=np.reshape(m,(self.nParam)) 843 | else: 844 | self.m = np.zeros(self.nParam) 845 | # Initialize second raw moment 846 | if np.sum(u) != 0.0: 847 | if np.size(u) != self.nParam: 848 | raise ValueError('Second raw moment dimension mismatch') 849 | else: 850 | self.u=np.reshape(u,(self.nParam)) 851 | else: 852 | self.u = np.zeros(self.nParam) 853 | 854 | def update(self): 855 | """ Perform one iteration of Adamax 856 | """ 857 | SGD.learningSchedule(self) 858 | # Moment updates 859 | self.m = self.beta1*self.m + (1.0-self.beta1)*self.grad # Update biased first moment estimate 860 | self.mHat = self.m/(1.0-self.beta1**(self.currentIter+1)) # Compute bias-corrected first moment estimate 861 | self.u = np.maximum(self.beta2*self.u,np.abs(self.grad)) 862 | # self.v = self.beta2*self.v + (1.0-self.beta2)*np.multiply(self.grad,self.grad) # Update biased second moment estimate 863 | # Parameter updates 864 | self.param = self.param - np.divide((self.etaCurrent*self.mHat),self.u) 865 | SGD.satisfyBounds(self) 866 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 867 | #print('One iteration of Adamax has been performed successfully!\n') 868 | 869 | def performIter(self): 870 | """ 871 | Performs all the iterations of Adamax 872 | """ 873 | # initialize progress bar 874 | printProgressBar(0, self.maxiter, prefix = self.alg, suffix = 'Complete', length = 25) 875 | self.t = time.clock() 876 | for i in range(self.iter,self.maxiter,1): 877 | if self.stop == True: 878 | break 879 | #print('iteration', i+1, 'out of', self.maxiter) 880 | self.update() 881 | self.currentIter = i+1 882 | # print progress bar 883 | SGD.printProgress(self) 884 | # Update the objective and gradient 885 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 886 | SGD.evaluateObjFn(self) 887 | SGD.evaluateGradFn(self) 888 | SGD.stopCrit(self) 889 | 890 | def getMoments(self): 891 | """ 892 | This returns the updated moments 893 | """ 894 | return self.m, self.v 895 | 896 | class Adadelta(SGD): 897 | """ 898 | ============================================================================== 899 | | ADADELTA class | 900 | | derived class from Stochastic Gradient Descent | 901 | ============================================================================== 902 | Initialization: 903 | add = Adadelta(gradHist, updatehist, rho, obj, grad, eta, param, 904 | iter, maxIter, objFun, gradFun, lowerBound, upperBound) 905 | NOTE: gradHist: historical information of gradients 906 | (array of dimension nparam-by-1) 907 | this should equal to zero for 1st iteration 908 | ============================================================================== 909 | Attributes: (all private) 910 | grad: Gradient information (array of dimension nParam-by-1) 911 | eta: learning rate = 1 by default 912 | param: the parameter vector (array of dimension nParam-by-1) 913 | nParam: number of parameters 914 | gradHist: gradient history accumulator (see the algorithm) 915 | updateHist: parameter update history accumulator 916 | epsilon: square-root of machine-precision 917 | (required to avoid division by zero) 918 | rho: exponential decay rate (0.95 may be a good choice) 919 | iter: iteration number (optional) 920 | maxIter: maximum iteration number (optional input, default = 1) 921 | objFun: function handle to evaluate the objective 922 | (not required for maxit = 1 ) 923 | gradFun: function handle to evaluate the gradient 924 | (not required for maxit = 1 ) 925 | lowerBound: lower bound for the parameters (optional input) 926 | upperBound: upper bound for the parameters (optional input) 927 | stopGrad: stopping criterion based on 2-norm of gradient vector 928 | (default 10^-6) 929 | alg: algorithm used 930 | __version__: version of the code 931 | ============================================================================== 932 | Methods: 933 | Public: 934 | performIter:performs all the iterations inside a for loop 935 | getGradHist:returns gradient history (default is zero) 936 | Inherited: 937 | getParam: returns the parameter values 938 | getObj: returns the current objective value 939 | getGrad: returns the current gradient information 940 | getParamHist: returns parameter update history 941 | Private: (should not be called outside this class file) 942 | __init__: initialization 943 | update: performs one iteration of Adadelta 944 | Inherited: 945 | evaluateObjFn: evaluates the objective function 946 | evaluateGradFn: evaluates the gradients 947 | satisfyBounds: satisfies the parameter bounds 948 | learningSchedule: learning schedule 949 | stopCrit: check stopping criteria 950 | ============================================================================== 951 | Reference: Zeiler, Matthew D. 952 | "Adadelta: an adaptive learning rate method." 953 | arXiv preprint arXiv:1212.5701 (2012). 954 | ============================================================================== 955 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 956 | ============================================================================== 957 | """ 958 | def __init__(self,gradHist=0.0,updateHist=0.0,rho=0.95,**kwargs): 959 | """ Initialize the Adadelta class object. 960 | This can be used to perform one iteration of Adadelta. 961 | """ 962 | self.alg = 'Adadelta' 963 | SGD.printAlg(self) 964 | SGD.__init__(self,**kwargs) 965 | self.epsilon=np.finfo(float).eps # The machine precision 966 | # Initialize gradient history 967 | if np.sum(gradHist) != 0.0: 968 | if np.size(gradHist) != self.nParam: 969 | raise ValueError('Gradient history dimension mismatch') 970 | else: 971 | self.gradHist=np.reshape(gradHist,(self.nParam)) 972 | else: 973 | self.gradHist = np.zeros(self.nParam) 974 | # Initialize parameter history 975 | if np.sum(updateHist) != 0.0: 976 | if np.size(updateHist) != self.nParam: 977 | raise ValueError('Gradient history dimension mismatch') 978 | else: 979 | self.updateHist=np.reshape(updateHist,(self.nParam)) 980 | else: 981 | self.updateHist = np.zeros(self.nParam) 982 | # Initialize rho 983 | self.rho = rho 984 | # Set eta to 1.0 985 | if self.eta!=1.0: 986 | print('Learning rate = ',self.eta,'!= 1.0\nSo, the learning rate is set to 1.0\n') 987 | self.eta = 1.0 988 | 989 | def update(self): 990 | """ 991 | Perform one iteration of Adadelta 992 | """ 993 | self.epsilon = 1e-6 994 | if self.currentIter<200: 995 | self.epsilon = 0.1 996 | else: 997 | self.epsilon = 1e-6 998 | SGD.learningSchedule(self) 999 | # update gradient history acccumulator 1000 | self.gradHist+=self.rho*self.gradHist+(1.0-self.rho)*np.multiply(self.grad,self.grad); # Sum of gradient history 1001 | # Perform one iteration of Adadelta 1002 | RMSdx = np.sqrt(self.updateHist)+self.epsilon 1003 | RMSg = np.sqrt(self.gradHist)+self.epsilon 1004 | updateParam = np.multiply((np.divide(RMSdx,RMSg)),self.grad) 1005 | self.param=self.param-self.etaCurrent*updateParam 1006 | SGD.satisfyBounds(self) 1007 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 1008 | #print('One iteration of Adadelta has been performed successfully!\n') 1009 | # update parameter history accumulator 1010 | self.updateHist = self.rho*self.updateHist+(1.0-self.rho)*np.multiply(updateParam,updateParam) 1011 | 1012 | def performIter(self): 1013 | """ 1014 | Performs all the iterations of Adadelta 1015 | """ 1016 | # initialize progress bar 1017 | printProgressBar(0, self.maxiter, prefix = self.alg, suffix = 'Complete', length = 25) 1018 | self.t = time.clock() 1019 | for i in range(self.iter,self.maxiter,1): 1020 | if self.stop == True: 1021 | break 1022 | #print('iteration', i+1, 'out of', self.maxiter) 1023 | self.update() 1024 | self.currentIter = i+1 1025 | # print progress bar 1026 | SGD.printProgress(self) 1027 | # Update the objective and gradient 1028 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 1029 | SGD.evaluateObjFn(self) 1030 | SGD.evaluateGradFn(self) 1031 | SGD.stopCrit(self) 1032 | 1033 | def getGradHist(self): 1034 | """ 1035 | This returns the gradient history 1036 | """ 1037 | return self.gradHist 1038 | 1039 | def getUpdateHist(self): 1040 | """ 1041 | This returns the parameter update history 1042 | """ 1043 | self.updateHist 1044 | 1045 | class Nadam(SGD): 1046 | """ 1047 | ============================================================================== 1048 | | Nesterov-accelerated Adaptive moment estimation (Nadam) class | 1049 | | derived class from Stochastic Gradient Descent | 1050 | ============================================================================== 1051 | Initialization: 1052 | nadm = Nadam(m, v, beta1, beta2, obj, grad, eta, param, iter, 1053 | maxIter, objFun, gradFun, lowerBound, upperBound) 1054 | 1055 | ============================================================================== 1056 | Attributes: (all private) 1057 | grad: Gradient information (array of dimension nParam-by-1) 1058 | eta: learning rate 1059 | param: the parameter vector (array of dimension nParam-by-1) 1060 | nParam: number of parameters 1061 | beta1, beta2: exponential decay rates in [0,1) 1062 | (default beta1 = 0.9, beta2 = 0.999) 1063 | m: First moment (array of dimension nParam-by-1) 1064 | v: Second raw moment (array of dimension nParam-by-1) 1065 | epsilon: square-root of machine-precision 1066 | (required to avoid division by zero) 1067 | iter: iteration number 1068 | maxIter: maximum iteration number (optional input, default = 1) 1069 | objFun: function handle to evaluate the objective 1070 | (not required for maxit = 1 ) 1071 | gradFun: function handle to evaluate the gradient 1072 | (not required for maxit = 1 ) 1073 | lowerBound: lower bound for the parameters (optional input) 1074 | upperBound: upper bound for the parameters (optional input) 1075 | stopGrad: stopping criterion based on 2-norm of gradient vector 1076 | (default 10^-6) 1077 | alg: algorithm used 1078 | __version__: version of the code 1079 | ============================================================================== 1080 | Methods: 1081 | Public: 1082 | performIter: performs all the iterations inside a for loop 1083 | getGradHist: returns gradient history (default is zero) 1084 | getMoments: returns history of moments 1085 | Inherited: 1086 | getParam: returns the parameter values 1087 | getObj: returns the current objective value 1088 | getGrad: returns the current gradient information 1089 | getParamHist: returns parameter update history 1090 | Private: (should not be called outside this class file) 1091 | __init__: initialization 1092 | update: performs one iteration of Adam 1093 | Inherited: 1094 | evaluateObjFn: evaluates the objective function 1095 | evaluateGradFn: evaluates the gradients 1096 | satisfyBounds: satisfies the parameter bounds 1097 | learningSchedule: learning schedule 1098 | stopCrit: check stopping criteria 1099 | ============================================================================== 1100 | Reference: Timothy Dozat. 1101 | "Incorporating Nesterov Momentum into Adam". 1102 | ICLR Workshop, (1):2013–2016, 2016. 1103 | ============================================================================== 1104 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 1105 | ============================================================================== 1106 | """ 1107 | def __init__(self,m = 0.0,v = 0.0,beta1 = 0.9,beta2 = 0.99,**kwargs): 1108 | # def __init__(self,grad,learningRate,parameters,numParam,gradHist,beta1,beta2): 1109 | """ Initialize the adagrad class object. 1110 | This can be used to perform one iteration of Adam. 1111 | """ 1112 | self.alg = 'Nadam' 1113 | SGD.printAlg(self) 1114 | self.beta1 = beta1 # decay rate (beta1 = 0.9 is a good suggestion) 1115 | self.beta2 = beta2 # decay rate (beta2 = 0.999 is a good suggetion) 1116 | self.epsilon=np.finfo(float).eps # The machine precision 1117 | SGD.__init__(self,**kwargs) 1118 | # Initialize first moment 1119 | if np.sum(m) != 0.0: 1120 | if np.size(m) != self.nParam: 1121 | raise ValueError('First moment dimension mismatch') 1122 | else: 1123 | self.m=np.reshape(m,(self.nParam)) 1124 | else: 1125 | self.m = np.zeros(self.nParam) 1126 | # Initialize second raw moment 1127 | if np.sum(v) != 0.0: 1128 | if np.size(v) != self.nParam: 1129 | raise ValueError('Second raw moment dimension mismatch') 1130 | else: 1131 | self.v=np.reshape(v,(self.nParam)) 1132 | else: 1133 | self.v = np.zeros(self.nParam) 1134 | 1135 | 1136 | def update(self): 1137 | """ 1138 | Perform one iteration of Nadam 1139 | """ 1140 | SGD.learningSchedule(self) 1141 | # Moment updates 1142 | self.m = self.beta1*self.m + (1.0-self.beta1)*self.grad # Update biased first moment estimate 1143 | self.mHat = self.m/(1.0-self.beta1**(self.currentIter+1)) # Compute bias-corrected first moment estimate 1144 | self.v = self.beta2*self.v + (1.0-self.beta2)*np.multiply(self.grad,self.grad) # Update biased second moment estimate 1145 | self.vHat = self.v/(1.0-self.beta2**(self.currentIter+1)) # Compute bias-corrected second moment estimate 1146 | # Parameter updates 1147 | mHat2 = self.beta1*self.mHat+(1.0-self.beta1)*self.grad/(1.0-self.beta1**(self.currentIter+1)) 1148 | self.param = self.param - np.divide((self.etaCurrent*mHat2),(np.sqrt(self.vHat))+self.epsilon) 1149 | SGD.satisfyBounds(self) 1150 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 1151 | #print('One iteration of Nadam has been performed successfully!\n') 1152 | 1153 | def performIter(self): 1154 | """ 1155 | Performs all the iterations of Nadam 1156 | """ 1157 | # initialize progress bar 1158 | printProgressBar(0, self.maxiter, prefix = self.alg, suffix = 'Complete', length = 25) 1159 | self.t = time.clock() 1160 | for i in range(self.iter,self.maxiter,1): 1161 | if self.stop == True: 1162 | break 1163 | #print('iteration', i+1, 'out of', self.maxiter) 1164 | self.update() 1165 | self.currentIter = i+1 1166 | # print progress bar 1167 | SGD.printProgress(self) 1168 | # Update the objective and gradient 1169 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 1170 | SGD.evaluateObjFn(self) 1171 | SGD.evaluateGradFn(self) 1172 | SGD.stopCrit(self) 1173 | 1174 | def getMoments(self): 1175 | """ 1176 | This returns the updated moments 1177 | """ 1178 | return self.m, self.v 1179 | 1180 | class SAG(SGD): 1181 | """ 1182 | ============================================================================== 1183 | | Stochastic Average Gradient (SAG) class | 1184 | | derived class from Stochastic Gradient Descent | 1185 | ============================================================================== 1186 | Initialization: 1187 | sag = SAG(nSamples, nTotSamples, fullGrad = 0.0, obj, grad, eta, param, 1188 | iter, maxIter, objFun, gradFun, lowerBound, upperBound) 1189 | 1190 | ============================================================================== 1191 | Attributes: (all private) 1192 | fullGrad: Full gradient information 1193 | (array of dimension nParam-by-nTotSamples) 1194 | eta: learning rate 1195 | param: the parameter vector (array of dimension nParam-by-1) 1196 | nParam: number of parameters 1197 | nTotSamples: total number of samples 1198 | nSamples: number of gradients updated at each iteration 1199 | iter: iteration number (optional) 1200 | maxIter: maximum iteration number (optional input, default = 1) 1201 | objFun: function handle to evaluate the objective 1202 | (not required for maxit = 1 ) 1203 | gradFun: function handle to evaluate the gradient 1204 | (not required for maxit = 1 ) 1205 | lowerBound: lower bound for the parameters (optional input) 1206 | upperBound: upper bound for the parameters (optional input) 1207 | stopGrad: stopping criterion based on 2-norm of gradient vector 1208 | (default 10^-6) 1209 | learnSched: learning schedule (constant, exponential or time-based, 1210 | default = constant) 1211 | lrParam: learning schedule parameter (default =0.1) 1212 | alg: algorithm used 1213 | __version__: version of the code 1214 | ============================================================================== 1215 | Methods: 1216 | Public: 1217 | performIter:performs all the iterations inside a for loop 1218 | getGradHist:returns gradient history (default is zero) 1219 | Inherited: 1220 | getParam: returns the parameter values 1221 | getObj: returns the current objective value 1222 | getGrad: returns the current gradient information 1223 | getParamHist: returns parameter update history 1224 | Private: (should not be called outside this class file) 1225 | __init__: initialization 1226 | update: performs one iteration of SAG 1227 | Inherited: 1228 | evaluateObjFn: evaluates the objective function 1229 | evaluateGradFn: evaluates the gradients 1230 | satisfyBounds: satisfies the parameter bounds 1231 | learningSchedule: learning schedule 1232 | stopCrit: check stopping criteria 1233 | ============================================================================== 1234 | Reference: Roux, Nicolas L., Mark Schmidt, and Francis R. Bach. 1235 | "A stochastic gradient method with an exponential convergence rate 1236 | for finite training sets." 1237 | Advances in neural information processing systems. 2012. 1238 | ============================================================================== 1239 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 1240 | ============================================================================== 1241 | """ 1242 | def __init__(self,nSamples,nTotSamples,fullGrad =0.0,**kwargs): 1243 | """ Initialize the SAG class object. 1244 | This can be used to perform one iteration of SAG. 1245 | """ 1246 | self.alg = 'SAG' 1247 | SGD.printAlg(self) 1248 | grad = fullGrad 1249 | SGD.__init__(self,**kwargs) 1250 | # Assign total number of samples 1251 | if type(nTotSamples) != int: 1252 | raise TypeError('nSamples not an integer value') 1253 | else: 1254 | self.nTotSamples = nTotSamples 1255 | # Assign number of samples to be replaced at each iteration 1256 | if type(nSamples) != int: 1257 | raise TypeError('nSamples not an integer value') 1258 | else: 1259 | self.nSamples = nSamples 1260 | # Initialize gradients 1261 | if np.sum(fullGrad) != 0: 1262 | if np.size(fullGrad)/nTotSamples != self.nParam: 1263 | raise ValueError('Full gradient dimension mismatch') 1264 | else: 1265 | fullGrad = np.reshape(fullGrad,(self.nParam,nTotSamples)) 1266 | else: 1267 | self.fullGrad = np.zeros((self.nParam,self.nTotSamples)) 1268 | try: 1269 | self.gradFun 1270 | except NameError: 1271 | print('Please provide gradient function name') 1272 | self.fullGrad, nprime = self.gradFun(self.param,self.nTotSamples) 1273 | self.grad = self.fullGrad 1274 | 1275 | def update(self): 1276 | """ 1277 | Perform one iteration of SAG 1278 | """ 1279 | if hasattr(self,'gradFun'): 1280 | batchGrad,nprime = self.gradFun(self.param,self.nSamples) 1281 | else: 1282 | nprime = np.random.choice(range(self.nTotSamples), self.nSamples, replace = False) 1283 | batchGrad = self.fullGrad[:,nprime] 1284 | # Perform one iteration of SAG 1285 | for i in range(self.nSamples): 1286 | #self.evaluateGradFn() 1287 | self.fullGrad[:,nprime[i]] = batchGrad[:,i] 1288 | 1289 | SGD.learningSchedule(self) 1290 | self.param=self.param-self.etaCurrent*np.mean(self.fullGrad,1) 1291 | #print(np.mean(self.fullGrad,1),self.param) 1292 | SGD.satisfyBounds(self) 1293 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 1294 | #print('One iteration of SAG has been performed successfully!\n') 1295 | 1296 | def performIter(self): 1297 | """ 1298 | Performs all the iterations of SAG 1299 | """ 1300 | # initialize progress bar 1301 | printProgressBar(0, self.maxiter, prefix = self.alg, suffix = 'Complete', length = 25) 1302 | self.t = time.clock() 1303 | for i in range(self.iter,self.maxiter,1): 1304 | if self.stop == True: 1305 | break 1306 | #print('iteration', i+1, 'out of', self.maxiter) 1307 | self.update() 1308 | self.currentIter = i+1 1309 | # print progress bar 1310 | SGD.printProgress(self) 1311 | # Update the objective and gradient 1312 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 1313 | SGD.evaluateObjFn(self) 1314 | SGD.stopCrit(self) 1315 | 1316 | 1317 | class minibatchSGD(SGD): 1318 | """ 1319 | ============================================================================== 1320 | | minibatch SGD class | 1321 | | derived class from Stochastic Gradient Descent | 1322 | ============================================================================== 1323 | Initialization: 1324 | mbsgd = minibatchSGD(nSamples, nTotSamples,newGrad = 0.0, 1325 | obj, grad, eta, param, iter, maxiter, 1326 | objFun, gradFun, lowerBound, upperBound) 1327 | 1328 | ============================================================================== 1329 | Attributes: 1330 | alg: minibatchSGD 1331 | eta: learning rate 1332 | param: the parameter vector (array of dimension nParam-by-1) 1333 | nParam: number of parameters 1334 | newGrad: gradient information 1335 | (array of dimension nParam-by-nSamples) 1336 | nSamples: number of gradients updated at each iteration 1337 | iter: iteration number (optional) 1338 | maxIter: maximum iteration number (optional input, default = 1) 1339 | objFun: function handle to evaluate the objective 1340 | (not required for maxit = 1 ) 1341 | gradFun: function handle to evaluate the gradient 1342 | (not required for maxit = 1 ) 1343 | lowerBound: lower bound for the parameters (optionalinput) 1344 | upperBound: upper bound for the parameters (optional input) 1345 | stopGrad: stopping criterion based on 2-norm of gradient vector 1346 | (default 10^-6) 1347 | learnSched: learning schedule (constant, exponential or time-based, 1348 | default = constant) 1349 | lrParam: learning schedule parameter (default =0.1) 1350 | alg: algorithm used 1351 | __version__: version of the code 1352 | ============================================================================== 1353 | Methods: 1354 | Public: 1355 | performIter: performs all the iterations inside a for loop 1356 | getGradHist: returns gradient history (default is zero) 1357 | Inherited: 1358 | getParam: returns the parameter values 1359 | getObj: returns the current objective value 1360 | getGrad: returns the current gradient information 1361 | getParamHist: returns parameter update history 1362 | Private: (should not be called outside this class file) 1363 | __init__: initialization 1364 | update: performs one iteration of minibatch SGD 1365 | Inherited: 1366 | evaluateObjFn: evaluates the objective function 1367 | evaluateGradFn: evaluates the gradients 1368 | satisfyBounds: satisfies the parameter bounds 1369 | learningSchedule: learning schedule 1370 | stopCrit: check stopping criteria 1371 | ============================================================================== 1372 | Reference: 1373 | ============================================================================== 1374 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 1375 | ============================================================================== 1376 | """ 1377 | def __init__(self,nSamples,nTotSamples = np.inf,newGrad = 0.0,**kwargs): 1378 | """ Initialize the minibatch SGD class object. 1379 | This can be used to perform one iteration of minibatch SGD. 1380 | """ 1381 | self.alg = 'minibatchSGD' 1382 | SGD.printAlg(self) 1383 | self.grad = newGrad 1384 | SGD.__init__(self,**kwargs) 1385 | # Assign number of samples used at each iteration 1386 | if type(nSamples) != int: 1387 | raise TypeError('nSamples not an integer value') 1388 | else: 1389 | self.nSamples = nSamples 1390 | # Total number of samples 1391 | if type(nTotSamples) != int: 1392 | raise TypeError('nTotSamples not an integer value') 1393 | else: 1394 | self.nTotSamples = nTotSamples 1395 | # Check for total number of samples 1396 | if nTotSamples < nSamples: 1397 | print('nTotSamples can not be smaller that nSamples\n') 1398 | print('nTotSamples = nSamples is set\n') 1399 | print('NOTE: performing a batch gradient descent') 1400 | elif nTotSamples == nSamples: 1401 | print('NOTE: performing a batch gradient descent') 1402 | elif nTotSamples < np.inf: 1403 | print('NOTE: performing a minibatch SGD with ', nSamples/nTotSamples*100, '% of total samples') 1404 | else: 1405 | print('NOTE: performing a minibatch SGD with ', nSamples, ' samples') 1406 | # Initialize new gradients 1407 | if np.sum(newGrad) != 0.0: 1408 | if np.size(newGrad)/nSamples != self.nParam: 1409 | raise ValueError('New gradient dimension mismatch') 1410 | else: 1411 | self.newGrad=np.reshape(newGrad,(self.nParam)) 1412 | else: 1413 | self.newGrad = np.zeros((self.nParam,self.nSamples)) 1414 | try: 1415 | self.gradFun 1416 | except NameError: 1417 | print('Please provide gradient function name') 1418 | self.newGrad, nprime = self.gradFun(self.param,self.nSamples) 1419 | 1420 | def update(self): 1421 | """ 1422 | Perform one iteration of minibatch SGD 1423 | """ 1424 | SGD.learningSchedule(self) 1425 | if self.maxiter>1: 1426 | self.newGrad,nprime = self.gradFun(self.param,self.nSamples) 1427 | # Perform one iteration of minibatch SGD 1428 | self.param=self.param-self.etaCurrent*np.mean(self.newGrad,1) 1429 | SGD.satisfyBounds(self) 1430 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 1431 | #print('One iteration of minibatch SGD has been performed successfully!\n') 1432 | 1433 | def performIter(self): 1434 | """ 1435 | Performs all the iterations of minibatch SGD 1436 | """ 1437 | # initialize progress bar 1438 | printProgressBar(0, self.maxiter, prefix = self.alg, suffix = 'Complete', length = 25) 1439 | self.t = time.clock() 1440 | for i in range(self.iter,self.maxiter,1): 1441 | if self.stop == True: 1442 | break 1443 | #print('iteration', i+1, 'out of', self.maxiter) 1444 | self.update() 1445 | self.currentIter = i+1 1446 | # print progress bar 1447 | SGD.printProgress(self) 1448 | # Update the objective and gradient 1449 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 1450 | SGD.evaluateObjFn(self) 1451 | SGD.stopCrit(self) 1452 | 1453 | class SVRG(SGD): 1454 | """ 1455 | ============================================================================== 1456 | | Stochastic variance reduced gradient (SVRG) class | 1457 | | derived class from Stochastic Gradient Descent | 1458 | ============================================================================== 1459 | Initialization: 1460 | opt = SVRG(nTotSamples, innerIter = 10, outerIter = 200, option = 1,obj, 1461 | grad, eta, param, iter, maxiter, objFun, gradFun) 1462 | 1463 | NOTE: option = 1 or 2 as suggested in the reference paper. 1464 | ============================================================================== 1465 | Attributes: 1466 | alg: SVRG 1467 | eta: learning rate 1468 | param: the parameter vector (array of dimension nParam-by-1) 1469 | nParam: number of parameters 1470 | fullGrad: Full gradient information 1471 | (array of dimension nParam-by-nTotSamples) 1472 | nTotSamples: total number of samples 1473 | innerIter: inner iteration 1474 | outerIter: outer iteration 1475 | iter: iteration number (optional input) 1476 | maxIter: maximum iteration number 1477 | (optional, default = innerIter*outerIter) 1478 | objFun: function handle to evaluate the objective 1479 | (not required for maxit = 1 ) 1480 | gradFun: function handle to evaluate the gradient 1481 | (not required for maxit = 1 ) 1482 | mu: average gradient in the outer iteration 1483 | paramBest: best estimate of the param in the oter iteration 1484 | lowerBound: lower bound for the parameters (optional input) 1485 | upperBound: upper bound for the parameters (optional input) 1486 | stopGrad: stopping criterion based on 2-norm of gradient vector 1487 | (default 10^-6) 1488 | alg: algorithm used 1489 | __version__: version of the code 1490 | ============================================================================== 1491 | Methods: 1492 | Public: 1493 | performOuterIter: performs all the iterations inside a for loop 1494 | getGradHist: returns gradient history (default is zero) 1495 | Inherited: 1496 | getParam: returns the parameter values 1497 | getObj: returns the current objective value 1498 | getGrad: returns the current gradient information 1499 | getParamHist: returns parameter update history 1500 | Private: (should not be called outside this class file) 1501 | __init__: initialization 1502 | innerUpdate: performs inner iterations of SVRG 1503 | Inherited: 1504 | evaluateObjFn: evaluates the objective function 1505 | evaluateGradFn: evaluates the gradients 1506 | satisfyBounds: satisfies the parameter bounds 1507 | learningSchedule: learning schedule 1508 | stopCrit: check stopping criteria 1509 | ============================================================================== 1510 | Reference: Johnson, Rie, and Tong Zhang. 1511 | "Accelerating stochastic gradient descent using predictive variance reduction." 1512 | Advances in neural information processing systems. 2013. 1513 | ============================================================================== 1514 | written by Subhayan De (email: Subhayan.De@colorado.edu), July, 2018. 1515 | ============================================================================== 1516 | """ 1517 | def __init__(self,nTotSamples, innerIter = 10, outerIter = 200, option = 1, **kwargs): 1518 | """ Initialize the SVRG class object. 1519 | This can be used to perform one iteration of SVRG. 1520 | """ 1521 | self.alg = 'SVRG' 1522 | SGD.printAlg(self) 1523 | SGD.__init__(self,**kwargs) 1524 | self.nTotSamples = nTotSamples 1525 | # Check inner iteration and outer iteration values 1526 | if innerIter*outerIter > self.maxiter: 1527 | self.maxiter = innerIter*outerIter 1528 | print('Maximum iteration number is set to ',self.maxiter) 1529 | self.innerIter = innerIter 1530 | self.outerIter = outerIter 1531 | self.paramBest = self.param 1532 | # Initialize gradients 1533 | try: 1534 | self.gradFun 1535 | except NameError: 1536 | print('Please provide gradient function name') 1537 | self.fullGrad, nprime = self.gradFun(self.param,self.nTotSamples) 1538 | self.grad = self.fullGrad 1539 | self.mu = np.mean(self.grad,1) 1540 | self.option = option 1541 | 1542 | def innerUpdate(self): 1543 | """ 1544 | Perform inner iterations of SVRG 1545 | """ 1546 | for i in range(self.innerIter): 1547 | SGD.learningSchedule(self) 1548 | it = np.random.randint(self.nTotSamples) 1549 | bestParamGrad, notNeeded = self.gradFun(self.paramBest,1) 1550 | bestParamGrad = np.reshape(bestParamGrad,(2)) 1551 | self.param = self.param - self.etaCurrent*(self.grad[:,it]-bestParamGrad+self.mu) 1552 | SGD.satisfyBounds(self) 1553 | self.paramHist = np.append(self.paramHist,np.reshape(self.param,(2,1)), axis = 1) 1554 | if self.option == 1: 1555 | 1556 | self.paramBest = self.param 1557 | else: 1558 | ind = np.random.randint(low = self.totIter, high = self.totIter+self.innerIter) 1559 | self.paramBest = self.paramHist[:,ind] 1560 | 1561 | def performOuterIter(self): 1562 | """ 1563 | Performs all the iterations of SVRG 1564 | """ 1565 | # initialize progress bar 1566 | printProgressBar(0, self.outerIter, prefix = self.alg, suffix = 'Complete', length = 25) 1567 | self.t = time.clock() 1568 | self.totIter = 0 1569 | for i in range(self.iter,self.outerIter,1): 1570 | if self.stop == True: 1571 | break 1572 | #print('Outer iteration', i+1, ' of', self.outerIter, ' (inner iteration = ', self.innerIter,')') 1573 | self.innerUpdate() 1574 | self.totIter = self.totIter + (i+1)*self.innerIter 1575 | self.currentIter = i+1 1576 | # print progress bar 1577 | SGD.printProgress(self) 1578 | self.grad, notNeeded = self.gradFun(self.paramBest,self.nTotSamples) 1579 | self.mu = np.mean(self.grad,1) 1580 | # Update the objective and gradient 1581 | if self.maxiter > 1: # since objFun and gradFun are optional for 1 iteration 1582 | SGD.evaluateObjFn(self) 1583 | SGD.stopCrit(self) 1584 | --------------------------------------------------------------------------------