├── images ├── score.png ├── stabilization ├── agent-environment.png ├── Cartpole-Architecture.png └── architecture_notebook.png ├── latex ├── images │ ├── kaist.png │ ├── plot_score.png │ ├── architecture.png │ ├── agent-environment.png │ ├── kaist_round_logo.png │ └── example_extracted_screen.png ├── references.bib └── main.tex ├── save_model ├── policy_net_best1.pt ├── policy_net_best2.pt ├── policy_net_best3.pt ├── target_net_best1.pt ├── target_net_best2.pt └── target_net_best3.pt ├── save_graph └── Cartpole_Vision_Stop-142_LastEpNum-20.png ├── Studies_on_Model_Free_Control_of_Dynamical_Systems.pdf ├── .gitignore ├── README.md ├── cartpole_vision_v1.py └── LICENSE /images/score.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fedebotu/vision-cartpole-dqn/HEAD/images/score.png -------------------------------------------------------------------------------- /images/stabilization: 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*.egg 26 | MANIFEST 27 | 28 | # PyInstaller 29 | # Usually these files are written by a python script from a template 30 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 31 | *.manifest 32 | *.spec 33 | 34 | # Installer logs 35 | pip-log.txt 36 | pip-delete-this-directory.txt 37 | 38 | # Unit test / coverage reports 39 | htmlcov/ 40 | .tox/ 41 | .coverage 42 | .coverage.* 43 | .cache 44 | nosetests.xml 45 | coverage.xml 46 | *.cover 47 | .hypothesis/ 48 | .pytest_cache/ 49 | 50 | # Translations 51 | *.mo 52 | *.pot 53 | 54 | # Django stuff: 55 | *.log 56 | local_settings.py 57 | db.sqlite3 58 | 59 | # Flask stuff: 60 | instance/ 61 | .webassets-cache 62 | 63 | # Scrapy stuff: 64 | .scrapy 65 | 66 | # Sphinx documentation 67 | docs/_build/ 68 | 69 | # PyBuilder 70 | target/ 71 | 72 | # Jupyter Notebook 73 | .ipynb_checkpoints 74 | 75 | # pyenv 76 | .python-version 77 | 78 | # celery beat schedule file 79 | celerybeat-schedule 80 | 81 | # SageMath parsed files 82 | *.sage.py 83 | 84 | # Environments 85 | .env 86 | .venv 87 | env/ 88 | venv/ 89 | ENV/ 90 | env.bak/ 91 | venv.bak/ 92 | 93 | # Spyder project settings 94 | .spyderproject 95 | .spyproject 96 | 97 | # Rope project settings 98 | .ropeproject 99 | 100 | # mkdocs documentation 101 | /site 102 | 103 | # mypy 104 | .mypy_cache/ 105 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Vision-Based CartPole with DQN 2 |

3 | Python 4 | PyTorch 5 |

6 | 7 | Implementation of the CartPole from OpenAI's Gym using only visual input 8 | for Reinforcement Learning control with Deep Q-Networks 9 | 10 |

11 | 12 |

13 | 14 | ***Author:*** Federico Berto 15 | 16 | Thesis Project for University of Bologna; 17 | Reinforcement Learning: a Preliminary Study on Vision-Based Control 18 | 19 | A special thanks goes to `Adam Paszke `_, 20 | for a first implementation of the DQN algorithm with vision input in 21 | the Cartpole-V0 environment from OpenAI Gym. 22 | `Gym website `__. 23 | 24 | The goal of this project is to design a control system for stabilizing a 25 | Cart and Pole using Deep Reinforcement Learning, having only images as 26 | control inputs. We implement the vision-based control using the DQN algorithm 27 | combined with Convolutional Neural Network for Q-values approximation. 28 | 29 |

30 | Agent Environment 31 |

32 | 33 | The last two frames of the Cartpole are used as input, cropped and processed 34 | before using them in the Neural Network. In order to stabilize the training, 35 | we use an experience replay buffer as shown in the paper "Playing Atari with 36 | Deep Reinforcement Learning: 37 | __. 38 | 39 | Besides, a target network to further stabilize the training process is used. 40 | make the training not converge, we set a threshold for stopping training 41 | when we detect stable improvements: this way we learn optimal behavior 42 | without saturation. 43 | 44 | 45 | ## Version 1 46 | 47 | This version is less polished and in a `.py` file. 48 | The GUI is a handy tool for saving and loading trained models, and also for 49 | training start/stop. Models and Graphs are saved in Vision_Carpole/save_model 50 | and Vision_Cartpole/save_graph respectively. 51 | 52 | 53 | ## Version 2 54 | This `.ipynb` (Jupyter Notebook) version is clearer and with a more stable training. 55 | The architecture is as following: 56 | 57 |

58 | DQN Architecture 59 |

60 | 61 | You may find more information inside the PDF report too. 62 | 63 |

64 | DQN Final Score over 6 Runs 65 |

66 | 67 | Final score averaged over 6 runs mean ± std 68 | 69 | If you want to improve this project, your help is always welcome! 😄 70 | 71 | 72 | -------------------------------------------------------------------------------- /latex/references.bib: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | @article{mnih2013playing, 5 | title={Playing atari with deep reinforcement learning}, 6 | author={Mnih, Volodymyr and Kavukcuoglu, Koray and Silver, David and Graves, Alex and Antonoglou, Ioannis and Wierstra, Daan and Riedmiller, Martin}, 7 | journal={arXiv preprint arXiv:1312.5602}, 8 | year={2013} 9 | } 10 | @article{DBLP:journals/corr/PintoDSG17, 11 | author = {Lerrel Pinto and 12 | James Davidson and 13 | Rahul Sukthankar and 14 | Abhinav Gupta}, 15 | title = {Robust Adversarial Reinforcement Learning}, 16 | journal = {CoRR}, 17 | volume = {abs/1703.02702}, 18 | year = {2017}, 19 | url = {http://arxiv.org/abs/1703.02702}, 20 | archivePrefix = {arXiv}, 21 | eprint = {1703.02702}, 22 | timestamp = {Fri, 05 Apr 2019 07:29:46 +0200}, 23 | biburl = {https://dblp.org/rec/journals/corr/PintoDSG17.bib}, 24 | bibsource = {dblp computer science bibliography, https://dblp.org} 25 | } 26 | @inproceedings{NEURIPS2018_69386f6b, 27 | author = {Chen, Ricky T. 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Lillicrap and 490 | Tim Harley and 491 | David Silver and 492 | Koray Kavukcuoglu}, 493 | title = {Asynchronous Methods for Deep Reinforcement Learning}, 494 | journal = {CoRR}, 495 | volume = {abs/1602.01783}, 496 | year = {2016}, 497 | url = {http://arxiv.org/abs/1602.01783}, 498 | archivePrefix = {arXiv}, 499 | eprint = {1602.01783}, 500 | timestamp = {Mon, 13 Aug 2018 16:47:40 +0200}, 501 | biburl = {https://dblp.org/rec/bib/journals/corr/MnihBMGLHSK16}, 502 | bibsource = {dblp computer science bibliography, https://dblp.org} 503 | } -------------------------------------------------------------------------------- /cartpole_vision_v1.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | ''' 3 | 4 | ***Author:*** Federico Berto 5 | 6 | ============= Thesis Project for University of Bologna ============= 7 | Reinforcement Learning: a Preliminary Study on Vision-Based Control 8 | 9 | A special thanks goes to gi`Adam Paszke `_, 10 | for a first implementation of the DQN algorithm with vision input in 11 | the Cartpole-V0 environment from OpenAI Gym. 12 | `Gym website `__. 13 | 14 | The goal of this project is to design a control system for stabilizing a 15 | Cart and Pole using Deep Reinforcement Learning, having only images as 16 | control inputs. We implement the vision-based control using the DQN algorithm 17 | combined with Convolutional Neural Network for Q-values approximation. 18 | 19 | The last two frames of the Cartpole are used as input, cropped and processed 20 | before using them in the Neural Network. In order to stabilize the training, 21 | we use an experience replay buffer as shown in the paper "Playing Atari with 22 | Deep Reinforcement Learning: 23 | __. 24 | 25 | Besides, a target network to further stabilize the training process is used. 26 | make the training not converge, we set a threshold for stopping training 27 | when we detect stable improvements: this way we learn optimal behavior 28 | without saturation. 29 | 30 | The GUI is a handi tool for saving and loading trained models, and also for 31 | training start/stop. Models and Graphs are saved in Vision_Carpole/save_model 32 | and Vision_Cartpole/save_graph respectively. 33 | 34 | ''' 35 | 36 | import gym 37 | import math 38 | import random 39 | import numpy as np 40 | import matplotlib 41 | import matplotlib.pyplot as plt 42 | from collections import namedtuple 43 | from itertools import count 44 | from PIL import Image 45 | import torch 46 | import torch.nn as nn 47 | import torch.optim as optim 48 | import torch.nn.functional as F 49 | import torchvision.transforms as T 50 | from collections import deque 51 | import tkinter 52 | 53 | ############ HYPERPARAMETERS ############## 54 | 55 | BATCH_SIZE = 128 # original = 128 56 | GAMMA = 0.999 # original = 0.999 57 | EPS_START = 0.9 # original = 0.9 58 | EPS_END = 0.05 # original = 0.05 59 | EPS_DECAY = 5000 # original = 200 60 | TARGET_UPDATE = 50 # original = 10 61 | MEMORY_SIZE = 100000 # original = 10000 62 | END_SCORE = 200 # 200 for Cartpole-v0 63 | TRAINING_STOP = 142 # threshold for training stop 64 | N_EPISODES = 50000 # total episodes to be run 65 | LAST_EPISODES_NUM = 20 # number of episodes for stopping training 66 | FRAMES = 2 # state is the number of last frames: the more frames, 67 | # the more the state is detailed (still Markovian) 68 | RESIZE_PIXELS = 60 # Downsample image to this number of pixels 69 | 70 | # ---- CONVOLUTIONAL NEURAL NETWORK ---- 71 | HIDDEN_LAYER_1 = 16 72 | HIDDEN_LAYER_2 = 32 73 | HIDDEN_LAYER_3 = 32 74 | KERNEL_SIZE = 5 # original = 5 75 | STRIDE = 2 # original = 2 76 | # -------------------------------------- 77 | 78 | GRAYSCALE = True # False is RGB 79 | LOAD_MODEL = False # If we want to load the model, Default= False 80 | USE_CUDA = False # If we want to use GPU (powerful one needed!) 81 | ############################################ 82 | 83 | graph_name = 'Cartpole_Vision_Stop-' + str(TRAINING_STOP) + '_LastEpNum-' + str(LAST_EPISODES_NUM) 84 | 85 | 86 | # GUI for saving models with Tkinter 87 | FONT = "Fixedsys 12 bold" #GUI font 88 | save_command1, save_command2, save_command3 = 0, 0, 0 89 | load_command_1, load_command_2, load_command_3 = 0, 0, 0 90 | resume_command, stop_command = 0,0 91 | window = tkinter.Tk() 92 | window.lift() 93 | window.attributes("-topmost", True) 94 | window.title("DQN-Vision Manager") 95 | lbl = tkinter.Label(window, text="Manage training -->") 96 | lbl.grid(column=0, row=0) 97 | 98 | def clicked1(): 99 | global save_command1 100 | lbl.configure(text="Model saved in slot 1!") 101 | save_command1 = True 102 | btn1 = tkinter.Button(window, text="Save 1", font= FONT, command=clicked1, bg= "gray") 103 | btn1.grid(column=1, row=0) 104 | 105 | def clicked2(): 106 | global save_command2 107 | lbl.configure(text="Model saved in slot 2!") 108 | save_command2 = True 109 | btn2 = tkinter.Button(window, text="Save 2", font= FONT,command=clicked2, bg= "gray") 110 | btn2.grid(column=2, row=0) 111 | 112 | def clicked3(): 113 | global save_command3 114 | lbl.configure(text="Model saved in slot 3!") 115 | save_command3 = True 116 | btn3 = tkinter.Button(window, text="Save Best", font= FONT, command=clicked3, bg= "gray") 117 | btn3.grid(column=3, row=0) 118 | 119 | def clicked_load1(): 120 | global load_command_1 121 | lbl.configure(text="Model loaded from slot 1!") 122 | load_command_1 = True 123 | load_btn1 = tkinter.Button(window, text="Load 1", font= FONT, command=clicked_load1, bg= "blue") 124 | load_btn1.grid(column=1, row=1) 125 | 126 | def clicked_load2(): 127 | global load_command_2 128 | lbl.configure(text="Model loaded from slot 2!") 129 | load_command_2 = True 130 | load_btn2 = tkinter.Button(window, text="Load 2", font= FONT, command=clicked_load2, bg= "blue") 131 | load_btn2.grid(column=2, row=1) 132 | 133 | def clicked_load3(): 134 | global load_command_3 135 | lbl.configure(text="Model loaded from slot 3!") 136 | load_command_3 = True 137 | load_btn3 = tkinter.Button(window, text="Load Best", font= FONT, command=clicked_load3, bg= "blue") 138 | load_btn3.grid(column=3, row=1) 139 | 140 | def clicked_resume(): 141 | global resume_command 142 | lbl.configure(text="Training resumed!") 143 | resume_command = True 144 | resume_btn = tkinter.Button(window, text="Resume Training", font= FONT, command=clicked_resume, bg= "green") 145 | resume_btn.grid(column=1, row=2) 146 | 147 | def clicked_stop(): 148 | global stop_command 149 | lbl.configure(text="Training stopped!") 150 | stop_command = True 151 | stop_btn = tkinter.Button(window, text="Stop Training", font= FONT, command=clicked_stop, bg= "red") 152 | stop_btn.grid(column=3, row=2) 153 | 154 | 155 | # Settings for GRAYSCALE / RGB 156 | if GRAYSCALE == 0: 157 | resize = T.Compose([T.ToPILImage(), 158 | T.Resize(RESIZE_PIXELS, interpolation=Image.CUBIC), 159 | T.ToTensor()]) 160 | 161 | nn_inputs = 3*FRAMES # number of channels for the nn 162 | else: 163 | resize = T.Compose([T.ToPILImage(), 164 | T.Resize(RESIZE_PIXELS, interpolation=Image.CUBIC), 165 | T.Grayscale(), 166 | T.ToTensor()]) 167 | nn_inputs = FRAMES # number of channels for the nn 168 | 169 | 170 | stop_training = False 171 | 172 | env = gym.make('CartPole-v0').unwrapped 173 | 174 | # Set up matplotlib 175 | is_ipython = 'inline' in matplotlib.get_backend() 176 | if is_ipython: 177 | from IPython import display 178 | 179 | plt.ion() 180 | 181 | # If gpu is to be used 182 | device = torch.device("cuda" if (torch.cuda.is_available() and USE_CUDA) else "cpu") 183 | 184 | Transition = namedtuple('Transition', 185 | ('state', 'action', 'next_state', 'reward')) 186 | 187 | # Memory for Experience Replay 188 | class ReplayMemory(object): 189 | 190 | def __init__(self, capacity): 191 | self.capacity = capacity 192 | self.memory = [] 193 | self.position = 0 194 | 195 | def push(self, *args): 196 | """Saves a transition.""" 197 | if len(self.memory) < self.capacity: 198 | self.memory.append(None) # if we haven't reached full capacity, we append a new transition 199 | self.memory[self.position] = Transition(*args) 200 | self.position = (self.position + 1) % self.capacity # e.g if the capacity is 100, and our position is now 101, we don't append to 201 | # position 101 (impossible), but to position 1 (its remainder), overwriting old data 202 | 203 | def sample(self, batch_size): 204 | return random.sample(self.memory, batch_size) 205 | 206 | def __len__(self): 207 | return len(self.memory) 208 | 209 | # Build CNN 210 | class DQN(nn.Module): 211 | 212 | def __init__(self, h, w, outputs): 213 | super(DQN, self).__init__() 214 | self.conv1 = nn.Conv2d(nn_inputs, HIDDEN_LAYER_1, kernel_size=KERNEL_SIZE, stride=STRIDE) 215 | self.bn1 = nn.BatchNorm2d(HIDDEN_LAYER_1) 216 | self.conv2 = nn.Conv2d(HIDDEN_LAYER_1, HIDDEN_LAYER_2, kernel_size=KERNEL_SIZE, stride=STRIDE) 217 | self.bn2 = nn.BatchNorm2d(HIDDEN_LAYER_2) 218 | self.conv3 = nn.Conv2d(HIDDEN_LAYER_2, HIDDEN_LAYER_3, kernel_size=KERNEL_SIZE, stride=STRIDE) 219 | self.bn3 = nn.BatchNorm2d(HIDDEN_LAYER_3) 220 | # Number of Linear input connections depends on output of conv2d layers 221 | # and therefore the input image size, so compute it. 222 | def conv2d_size_out(size, kernel_size = 5, stride = 2): 223 | return (size - (kernel_size - 1) - 1) // stride + 1 224 | convw = conv2d_size_out(conv2d_size_out(conv2d_size_out(w))) 225 | convh = conv2d_size_out(conv2d_size_out(conv2d_size_out(h))) 226 | linear_input_size = convw * convh * 32 227 | nn.Dropout() 228 | self.head = nn.Linear(linear_input_size, outputs) 229 | 230 | # Called with either one element to determine next action, or a batch 231 | # during optimization. Returns tensor([[left0exp,right0exp]...]). 232 | def forward(self, x): 233 | x = F.relu(self.bn1(self.conv1(x))) 234 | x = F.relu(self.bn2(self.conv2(x))) 235 | x = F.relu(self.bn3(self.conv3(x))) 236 | return self.head(x.view(x.size(0), -1)) 237 | 238 | # Cart location for centering image crop 239 | def get_cart_location(screen_width): 240 | world_width = env.x_threshold * 2 241 | scale = screen_width / world_width 242 | return int(env.state[0] * scale + screen_width / 2.0) # MIDDLE OF CART 243 | 244 | # Cropping, downsampling (and Grayscaling) image 245 | def get_screen(): 246 | # Returned screen requested by gym is 400x600x3, but is sometimes larger 247 | # such as 800x1200x3. Transpose it into torch order (CHW). 248 | screen = env.render(mode='rgb_array').transpose((2, 0, 1)) 249 | # Cart is in the lower half, so strip off the top and bottom of the screen 250 | _, screen_height, screen_width = screen.shape 251 | screen = screen[:, int(screen_height*0.4):int(screen_height * 0.8)] 252 | view_width = int(screen_width * 0.6) 253 | cart_location = get_cart_location(screen_width) 254 | if cart_location < view_width // 2: 255 | slice_range = slice(view_width) 256 | elif cart_location > (screen_width - view_width // 2): 257 | slice_range = slice(-view_width, None) 258 | else: 259 | slice_range = slice(cart_location - view_width // 2, 260 | cart_location + view_width // 2) 261 | # Strip off the edges, so that we have a square image centered on a cart 262 | screen = screen[:, :, slice_range] 263 | # Convert to float, rescale, convert to torch tensor 264 | # (this doesn't require a copy) 265 | screen = np.ascontiguousarray(screen, dtype=np.float32) / 255 266 | screen = torch.from_numpy(screen) 267 | # Resize, and add a batch dimension (BCHW) 268 | return resize(screen).unsqueeze(0).to(device) 269 | 270 | 271 | env.reset() 272 | plt.figure() 273 | if GRAYSCALE == 0: 274 | plt.imshow(get_screen().cpu().squeeze(0).permute(1, 2, 0).numpy(), 275 | interpolation='none') 276 | else: 277 | plt.imshow(get_screen().cpu().squeeze(0).permute( 278 | 1, 2, 0).numpy().squeeze(), cmap='gray') 279 | plt.title('Example extracted screen') 280 | plt.show() 281 | 282 | 283 | 284 | 285 | eps_threshold = 0.9 # original = 0.9 286 | 287 | init_screen = get_screen() 288 | _, _, screen_height, screen_width = init_screen.shape 289 | print("Screen height: ", screen_height," | Width: ", screen_width) 290 | 291 | # Get number of actions from gym action space 292 | n_actions = env.action_space.n 293 | 294 | policy_net = DQN(screen_height, screen_width, n_actions).to(device) 295 | target_net = DQN(screen_height, screen_width, n_actions).to(device) 296 | target_net.load_state_dict(policy_net.state_dict()) 297 | target_net.eval() 298 | 299 | if LOAD_MODEL == True: 300 | policy_net_checkpoint = torch.load('save_model/policy_net_best3.pt') # best 3 is the default best 301 | target_net_checkpoint = torch.load('save_model/target_net_best3.pt') 302 | policy_net.load_state_dict(policy_net_checkpoint) 303 | target_net.load_state_dict(target_net_checkpoint) 304 | policy_net.eval() 305 | target_net.eval() 306 | stop_training = True # if we want to load, then we don't train the network anymore 307 | 308 | optimizer = optim.RMSprop(policy_net.parameters()) 309 | memory = ReplayMemory(MEMORY_SIZE) 310 | 311 | steps_done = 0 312 | 313 | # Action selection , if stop training == True, only exploitation 314 | def select_action(state, stop_training): 315 | global steps_done 316 | sample = random.random() 317 | eps_threshold = EPS_END + (EPS_START - EPS_END) * \ 318 | math.exp(-1. * steps_done / EPS_DECAY) 319 | steps_done += 1 320 | # print('Epsilon = ', eps_threshold, end='\n') 321 | if sample > eps_threshold or stop_training: 322 | with torch.no_grad(): 323 | # t.max(1) will return largest column value of each row. 324 | # second column on max result is index of where max element was 325 | # found, so we pick action with the larger expected reward. 326 | return policy_net(state).max(1)[1].view(1, 1) 327 | else: 328 | return torch.tensor([[random.randrange(n_actions)]], device=device, dtype=torch.long) 329 | 330 | 331 | episode_durations = [] 332 | 333 | 334 | # Plotting 335 | def plot_durations(score): 336 | plt.figure(2) 337 | plt.clf() 338 | durations_t = torch.tensor(episode_durations, dtype=torch.float) 339 | episode_number = len(durations_t) 340 | plt.title('Training...') 341 | plt.xlabel('Episode') 342 | plt.ylabel('Duration') 343 | plt.plot(durations_t.numpy(), label= 'Score') 344 | matplotlib.pyplot.hlines(195, 0, episode_number, colors='red', linestyles=':', label='Win Threshold') 345 | # Take 100 episode averages and plot them too 346 | if len(durations_t) >= 100: 347 | means = durations_t.unfold(0, 100, 1).mean(1).view(-1) 348 | last100_mean = means[episode_number -100].item() 349 | means = torch.cat((torch.zeros(99), means)) 350 | plt.plot(means.numpy(), label= 'Last 100 mean') 351 | print('Episode: ', episode_number, ' | Score: ', score, '| Last 100 mean = ', last100_mean) 352 | plt.legend(loc='upper left') 353 | #plt.savefig('./save_graph/cartpole_dqn_vision_test.png') # for saving graph with latest 100 mean 354 | plt.pause(0.001) # pause a bit so that plots are updated 355 | plt.savefig('save_graph/' + graph_name) 356 | if is_ipython: 357 | display.clear_output(wait=True) 358 | display.display(plt.gcf()) 359 | 360 | # Training 361 | def optimize_model(): 362 | if len(memory) < BATCH_SIZE: 363 | return 364 | transitions = memory.sample(BATCH_SIZE) 365 | # Transpose the batch (see https://stackoverflow.com/a/19343/3343043 for 366 | # detailed explanation). This converts batch-array of Transitions 367 | # to Transition of batch-arrays. 368 | batch = Transition(*zip(*transitions)) 369 | 370 | # Compute a mask of non-final states and concatenate the batch elements 371 | # (a final state would've been the one after which simulation ended) 372 | non_final_mask = torch.tensor(tuple(map(lambda s: s is not None, 373 | batch.next_state)), device=device, dtype=torch.uint8) 374 | non_final_next_states = torch.cat([s for s in batch.next_state 375 | if s is not None]) 376 | # torch.cat concatenates tensor sequence 377 | state_batch = torch.cat(batch.state) 378 | action_batch = torch.cat(batch.action) 379 | reward_batch = torch.cat(batch.reward) 380 | 381 | # Compute Q(s_t, a) - the model computes Q(s_t), then we select the 382 | # columns of actions taken. These are the actions which would've been taken 383 | # for each batch state according to policy_net 384 | state_action_values = policy_net(state_batch).gather(1, action_batch) 385 | 386 | # Compute V(s_{t+1}) for all next states. 387 | # Expected values of actions for non_final_next_states are computed based 388 | # on the "older" target_net; selecting their best reward with max(1)[0]. 389 | # This is merged based on the mask, such that we'll have either the expected 390 | # state value or 0 in case the state was final. 391 | next_state_values = torch.zeros(BATCH_SIZE, device=device) 392 | next_state_values[non_final_mask] = target_net(non_final_next_states).max(1)[0].detach() 393 | # Compute the expected Q values 394 | expected_state_action_values = (next_state_values * GAMMA) + reward_batch 395 | 396 | # Compute Huber loss 397 | loss = F.smooth_l1_loss(state_action_values, expected_state_action_values.unsqueeze(1)) 398 | plt.figure(2) 399 | 400 | # Optimize the model 401 | optimizer.zero_grad() 402 | loss.backward() 403 | for param in policy_net.parameters(): 404 | param.grad.data.clamp_(-1, 1) 405 | optimizer.step() 406 | 407 | mean_last = deque([0] * LAST_EPISODES_NUM, LAST_EPISODES_NUM) 408 | 409 | # Button click checking 410 | 411 | def check_button(): 412 | global save_command1 413 | global save_command2 414 | global save_command3 415 | global load_command_1 416 | global load_command_2 417 | global load_command_3 418 | global resume_command 419 | global stop_command 420 | global stop_training 421 | 422 | # Saving the weights 423 | if save_command1 == True: 424 | torch.save(policy_net.state_dict(), 'save_model/policy_net_best1.pt') # we save the trained policy model 425 | torch.save(target_net.state_dict(), 'save_model/target_net_best1.pt') # we save the trained target model 426 | save_command1 = False 427 | if save_command2 == True: 428 | torch.save(policy_net.state_dict(), 'save_model/policy_net_best2.pt') # we save the trained policy model 429 | torch.save(target_net.state_dict(), 'save_model/target_net_best2.pt') # we save the trained target model 430 | save_command2 = False 431 | if save_command3 == True: 432 | torch.save(policy_net.state_dict(), 'save_model/policy_net_best3.pt') # we save the trained policy model 433 | torch.save(target_net.state_dict(), 'save_model/target_net_best3.pt') # we save the trained target model 434 | save_command3 = False 435 | # Loading the Weights 436 | if load_command_1 or load_command_2 or load_command_3: 437 | if load_command_1: 438 | policy_net_checkpoint = torch.load('save_model/policy_net_best1.pt') 439 | target_net_checkpoint = torch.load('save_model/target_net_best1.pt') 440 | load_command_1 = False 441 | if load_command_2: 442 | policy_net_checkpoint = torch.load('save_model/policy_net_best2.pt') 443 | target_net_checkpoint = torch.load('save_model/target_net_best2.pt') 444 | load_command_2 = False 445 | if load_command_3: 446 | policy_net_checkpoint = torch.load('save_model/policy_net_best3.pt') 447 | target_net_checkpoint = torch.load('save_model/target_net_best3.pt') 448 | load_command_3 = False 449 | 450 | policy_net.load_state_dict(policy_net_checkpoint) 451 | target_net.load_state_dict(target_net_checkpoint) 452 | policy_net.eval() 453 | target_net.eval() 454 | stop_training = True # if we want to load, then we don't train the network anymore 455 | 456 | # Training Start/Stop 457 | if resume_command == True: 458 | stop_training = False 459 | resume_command = False 460 | if stop_command == True: 461 | stop_training = True 462 | stop_command = False 463 | 464 | window.attributes("-topmost", False) 465 | 466 | 467 | # MAIN LOOP 468 | 469 | for i_episode in range(N_EPISODES): 470 | # Initialize the environment and state 471 | env.reset() 472 | init_screen = get_screen() 473 | screens = deque([init_screen] * FRAMES, FRAMES) 474 | state = torch.cat(list(screens), dim=1) 475 | 476 | for t in count(): 477 | 478 | # Select and perform an action 479 | action = select_action(state, stop_training) 480 | state_variables, _, done, _ = env.step(action.item()) 481 | 482 | # Observe new state 483 | screens.append(get_screen()) 484 | next_state = torch.cat(list(screens), dim=1) if not done else None 485 | 486 | # Reward modification for better stability 487 | x, x_dot, theta, theta_dot = state_variables 488 | r1 = (env.x_threshold - abs(x)) / env.x_threshold - 0.8 489 | r2 = (env.theta_threshold_radians - abs(theta)) / env.theta_threshold_radians - 0.5 490 | reward = r1 + r2 491 | reward = torch.tensor([reward], device=device) 492 | if t >= END_SCORE-1: 493 | reward = reward + 20 494 | done = 1 495 | else: 496 | if done: 497 | reward = reward - 20 498 | 499 | # Store the transition in memory 500 | memory.push(state, action, next_state, reward) 501 | 502 | # Move to the next state 503 | state = next_state 504 | 505 | # Perform one step of the optimization (on the target network) 506 | if done: 507 | check_button() # We check the GUI for inputs 508 | episode_durations.append(t + 1) 509 | plot_durations(t + 1) 510 | mean_last.append(t + 1) 511 | mean = 0 512 | for i in range(LAST_EPISODES_NUM): 513 | mean = mean_last[i] + mean 514 | mean = mean/LAST_EPISODES_NUM 515 | if mean < TRAINING_STOP and stop_training == False: 516 | optimize_model() 517 | else: 518 | stop_training = 1 519 | break 520 | 521 | # Update the target network, copying all weights and biases in DQN 522 | if i_episode % TARGET_UPDATE == 0: 523 | target_net.load_state_dict(policy_net.state_dict()) 524 | 525 | print('Complete') 526 | env.render() 527 | env.close() 528 | plt.ioff() 529 | plt.show() -------------------------------------------------------------------------------- /latex/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | \usepackage[]{babel} 3 | \usepackage{natbib} 4 | \usepackage{url} 5 | \usepackage[utf8x]{inputenc} 6 | \usepackage{amsmath} 7 | \DeclareMathOperator*{\argmax}{argmax} % thin space, limits underneath in displays 8 | \DeclareMathOperator*{\argmin}{argmin} % thin space, limits underneath in displays 9 | \usepackage{graphicx} 10 | \graphicspath{{images/}} 11 | \usepackage{parskip} 12 | \usepackage{fancyhdr} 13 | \usepackage{vmargin} 14 | \usepackage{breqn} % Automatic equation breaker 15 | \usepackage{amssymb} %% <- for \square and \blacksquare 16 | \usepackage{breqn} % used for automatic equation breaking 17 | \newcommand{\QEDA}{\null\nobreak\hfill\ensuremath{\blacksquare}}% 18 | \newcommand{\QEDB}{\null\nobreak\hfill\ensuremath{\square}}% 19 | \newcommand{\smallspace}{\hspace{0.5cm}} 20 | \setcounter{secnumdepth}{0} % for avoiding the numbering 21 | \usepackage{hyperref} % to click and go to pointed place in the document 22 | \usepackage{tcolorbox} % if we want to use the boxes 23 | \usepackage{cancel} % for cool cancellations 24 | \newenvironment{sfemph}{\begin{sffamily}\begin{emph}}{\end{sffamily}\end{emph}} 25 | % the text inside the exercise setup will be emphasized 26 | \usepackage{xcolor} % Colored text 27 | \usepackage{minted} % For highlighting Python code 28 | \usepackage[ruled,vlined]{algorithm2e} % for algorithms 29 | \usepackage{biblatex} % bibliography 30 | \addbibresource{references.bib} 31 | 32 | % Set defaults for minted 33 | \setminted{frame=lines, 34 | framesep=2mm, 35 | baselinestretch=1.2, 36 | bgcolor=, 37 | fontsize=\footnotesize, 38 | linenos 39 | } 40 | \usepackage{comment} %for multiline commenting 41 | 42 | 43 | 44 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 45 | % MODIFY KAIST TEMPLATE DATA HERE 46 | 47 | \title{Studies on Model-Free Control of Dynamical Systems with Visual Feedback} 48 | \author{Federico Berto} 49 | \date{\today} 50 | \newcommand{\professor}{***} 51 | \newcommand{\studentid}{***} 52 | \newcommand{\coursename}{Optimal Control} 53 | \newcommand{\courseid}{***} 54 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 55 | 56 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 57 | \setmarginsrb{3 cm}{2.5 cm}{3 cm}{2.5 cm}{1 cm}{1.5 cm}{1 cm}{1.5 cm} 58 | 59 | \makeatletter 60 | \let\thetitle\@title 61 | \let\theauthor\@author 62 | \let\thedate\@date 63 | \makeatother 64 | 65 | \pagestyle{fancy} 66 | \fancyhf{} 67 | \renewcommand{\headrulewidth}{0.4pt}% Default \headrulewidth is 0.4pt 68 | %\renewcommand{\footrulewidth}{0.4pt}% Default \footrulewidth is 0pt 69 | \rhead{\theauthor} 70 | %\rhead{\includegraphics[width=1cm]{example-image-a}} 71 | \lhead{Optimal Control Report} 72 | \chead{\raisebox{-1ex}{\includegraphics[width = 3cm, shift down = 1cm]{kaist.png}}} 73 | \cfoot{Page \thepage} 74 | 75 | \begin{document} 76 | 77 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 78 | 79 | \begin{titlepage} 80 | \centering 81 | \textsc{\LARGE Korea Advanced Institute of Science \\ \smallskip and Technology}\\[1 cm] % University Name 82 | \includegraphics[scale = 0.18]{kaist_round_logo.png}\\[1.5 cm] % University Logo 83 | \textsc{\Large \coursename}\\[0.5 cm] % Course Code 84 | \rule{\linewidth}{0.2 mm} \\[0.4 cm] 85 | { \huge \bfseries {\thetitle}}\\ 86 | \rule{\linewidth}{0.2 mm} \\[1.5 cm] 87 | 88 | 89 | \begin{minipage}{0.5\textwidth} 90 | \begin{flushleft} \large 91 | \emph{Professor:}\\ 92 | \professor \\ [0.5cm] 93 | \emph{Course ID:}\\ 94 | \courseid 95 | \end{flushleft} 96 | \end{minipage}~ 97 | \begin{minipage}{0.4\textwidth} 98 | 99 | \begin{flushright} \large 100 | \emph{Student:} \\ 101 | \theauthor \\[0.5cm] 102 | \emph{ID number:}\\ 103 | \studentid \\ 104 | \end{flushright} 105 | 106 | \end{minipage}\\[2 cm] 107 | 108 | 109 | %\thedate 110 | 111 | 112 | 113 | \end{titlepage} 114 | 115 | % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 116 | 117 | % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 118 | \begin{abstract} 119 | Modeling is well know to be one of the most difficult challenges when developing control systems: partial observability and disturbances in the control system can make the system unstable; especially considering the cases of complex and nonlinear ones. Model-free control is an alternative for solving control problems without the need to design a complex model in the first place: in particular, Reinforcement Learning has shown promising results in controlling nonlinear systems even when the state variables cannot be derived directly, such as in the case of a system in which sensors are unavailable or broken. The goal of this report is to demonstrate the ability of Deep Q-Network algorithm in controlling a dynamical system with the aim of stabilizing an inverted pendulum using only raw pixels as state feedback: this model-free formulation does not require any assumption or previous knowledge of the dynamical system unlike most controllers. 120 | 121 | \end{abstract} 122 | 123 | 124 | \section{Introduction} 125 | 126 | Reinforcement Learning \cite{sutton1998introduction} is one of the branches of Machine Learning which has seen a surge in interest in recent years because of its ability to handle complex tasks with minimal human intervention and, in the case of model-free reinforcement learning, to learn a representation of the state-action space without needing the actual space variables.\\ 127 | Reinforcement Learning (RL) has been successfully used for playing complex Atari games \cite{mnih2013playing}, for mastering the game of GO \cite{Silver_2016} and even Starcraft II \cite{Starcraft}, showing important results regarding high-dimensional state-action spaces.\\ 128 | Another interesting application is the model-free control, which is still an open research topic \cite{DBLP:journals/corr/abs-1912-03513} given the complex nature of the continuous state: we will explore this setup in the report and show its promising capabilities in handling non-linear systems without the need of an explicit model formulation, unlike many controllers do. \\ 129 | Moreover, we will show that the performance of the controller is better, to the best of the author's knowledge, than other similar setups of the raw-pixels based inverted pendulum thanks to some tweaks we will explore. 130 | 131 | \section{Brief Overview of Reinforcement Learning} 132 | The control system can be defined as in the Figure \ref{fig:agentenvironment}, usually called the \textit{agent-environment interface}, which is the correspondent of the controller-plant interface in classical control. This framework can be defined by the following: 133 | 134 | \begin{figure}[h] 135 | \centering 136 | \includegraphics[width=12cm]{agent-environment.png} 137 | \caption{Agent-Environment interface for the inverted pendulum system. $\pi^*_{ \{ a \mid s \} }$ denotes the optimal policy} 138 | \label{fig:agentenvironment} 139 | \end{figure} 140 | 141 | \begin{itemize} 142 | \item \textit{Policy}: set of \textit{actions} (which are the control inputs in the Optimal Control field) to be selected given the current state. 143 | \item \textit{Reward}: a scalar value to be maximized by the agent. This value is another feedback along with the state at each time step; this is usually set as a positive number if the agent is performing as desired and as a negative number otherwise. In the Optimal Control terms, it is equivalent to the opposite of the cost function. 144 | \item \textit{Value function}: whereas the reward defines what is good in a short time, the value function defines what is good in the long run; it is defined as the sum of the discounted future rewards that can be accumulated from a particular state. 145 | \end{itemize} 146 | 147 | The goal of the control system (agent) is to maximize the cumulative discounted reward defined as following from the environment: 148 | 149 | \begin{equation} 150 | G_t = R_{t+1} + \gamma R_{t+2} + ... = \sum_{k=0}^{\infty}\gamma^k R_{t+k+1} 151 | \end{equation} 152 | where $\gamma \in [0,1]$ is a discount factor used for giving a lighter weight to far-away future rewards. \\ 153 | The policy $\pi$ choosing the actions leading to the highest reward can be chosen for the Deep Q-Networks in the \textit{$\varepsilon$-greedy} way: 154 | \begin{equation} 155 | \pi(a|s) = \begin{cases} 156 | 1 - \varepsilon, & \text{if $a = \argmax_{a \in \mathcal{A}} \, q^*(s,a)$}\\ 157 | \varepsilon, & \text{a random action}. 158 | \end{cases} 159 | \end{equation} 160 | where $q^*(s,a)$ denotes the \textit{state-action value} and $\varepsilon$ is chosen depending on how much \textit{exploration} (randomly trying new actions for finding out undiscovered and possibly better states and actions) and \textit{exploitation} (choosing the known best action) ration we want the system to have. 161 | 162 | \paragraph{Trajectories of the system} 163 | In order to optimize the system, we need to know what trajectories lead to the best cumulative reward. In this setup, \textit{agent} is the entity acting on the \textit{environment}, that given a $state \ S_t \in \mathcal{S}$ selects one or more $actions \ A_t \in \mathcal{A}$ for interacting with the environment. Our agent then gets feedback from the environment itself: it gets a scalar valued $reward \ R_{t+1} \in \mathcal{R}$, and gets in a new state $S_{t+1} \in \mathcal{S}$. In a \textit{finite} Markov Decision Process the set of states, actions and rewards ($\mathcal{S},\mathcal{A},\mathcal{R})$ contains a finite number of elements; nonetheless, the problem can be extended in the continuous case. The agent-environment feedback loop repeats over time and it is updated at each time \textit{step}: action selection, state and reward signals are sent only at specific moments in time (t = 0,1,2,3...). The sequence of actions, states and rewards defines a \textit{trajectory} in time that can be described as: 164 | \begin{equation} 165 | S_0, A_0, R_1, S_1, A_1, R_2, S_2, A_2, R_3... 166 | \end{equation} 167 | This sequence can be used on the go for optimizing the system or stored in a buffer and used later in randomized batches allowing for better stability of the training. 168 | 169 | 170 | \section{Experimental Setup} 171 | 172 | We will conduct the experiments with the inverted pendulum simulation from OpenAI Gym \cite{brockman2016openai}. Also known as the \textit{cart-pole}, the inverted pendulum is a common benchmark for testing control systems because of its relative simplicity and yet challenging feat because of the system's nonlinearities. This system can be controlled with well-known controllers, such as the Linear Quadratic Regulator for the linearized version, or with i.e. the Model Predictive Control for the non-linear version, such as for the pendulum swing up; however, our task is more challenging because of the absence of the system's model. 173 | 174 | \begin{table} 175 | \centering 176 | \begin{tabular}{ |p{2cm}|p{4cm}|p{2cm}|p{2cm}| } 177 | \hline 178 | \multicolumn{4}{|c|}{Observation Space} \\ 179 | \hline 180 | Num & Observation & Min & Max \\ 181 | \hline 182 | 0 & Cart Position & -2.4 & 2.4 \\ 183 | 1 & Cart Velocity & $-\infty$ & $+\infty$ \\ 184 | 2 & Pole Angle & $\-41.8$\textdegree & $41.8$\textdegree \\ 185 | 3 & Pole Angular Velocity & $-\infty$ & $\infty$ \\ 186 | \hline 187 | \end{tabular} 188 | \label{table:tableenvironment} 189 | \caption{Inverted Pendulum's observation space} 190 | \end{table} 191 | 192 | \paragraph{The observations space} The simulation is made of a four dimensional observation space of the cart position, cart velocity, pole angle, and pole angular velocity as shown in Table \ref{table:tableenvironment}. 193 | 194 | The available actions are two discrete ones: push a cart left or right. The reward is defined as +1 for every time step the inverted pendulum stands including the termination step. The task is considered achieved when the average reward of the last 100 episodes reaches a score close to the maximum score of 200. Episode termination occurs when: 195 | 196 | \begin{itemize} 197 | \item The pole angle is more than $\pm 12$\textdegree 198 | \item The cart position is more than $\pm 2.4$ (i.e. the center of the cart almost reaches the edge of the display) 199 | \item The episode length is greater than 200 200 | \end{itemize} 201 | 202 | Although the observation space is fixed for the simulation, our vision-based control is based on a set of images of the simulation, which significantly increase the state observation size. In order to let the algorithm derive a good approximation of the state, we will use a sequence of the last $N$ images (i.e., the last 2 frames) for making it capable to infer the dynamics of the pendulum. 203 | 204 | \paragraph{The Algorithm: Deep Q-Learning} 205 | 206 | The Deep Q-Learning algorithm has shown state-of-the-art performance in multiple frameworks, such as the Atari framework \cite{mnih2013playing}. 207 | In order to approximate the action-value function, we will employ a Convolutional Neural Network $Q(s,a; \theta) \approx Q^*(s,a)$. For our purposes, $\theta$ will denote the set of weights of the network, which we will refer to as Q-network. A Q-network can be trained by minimizing a sequence of loss functions $L_i(\theta_i)$ changing at each iteration i, 208 | 209 | \begin{equation} 210 | L_i(\theta_i) = \mathbb{E}_{s,a \sim \rho(\cdot)}[\left(y_i - Q(s,a;\theta_i)\right)^2], 211 | \label{eq:lossfunction} 212 | \end{equation} 213 | 214 | where $y_i = \mathbb{E}_{s' \sim \mathcal{E}} [r + \gamma \max_{a'}Q(s', \theta_{i-1}) | s,a]$ is the target for iteration $i$, $\rho(s,a)$ is a probability distribution over sequences $s$ and actions $a$. The parameters from the previous iteration $\theta_{i-1}$ are kept fixed when optimizing the loss function $L_i(\theta_i)$. The targets depend on the network weights: for this reason, it differs from classical weights used in supervised learning, which are fixed before learning itself begins. 215 | \medskip 216 | 217 | \indent Since we want to minimize the loss function for obtaining a better fit of the networks with respect to the real action value function, we want to compute the gradient with respect to the weights: 218 | 219 | \begin{equation} 220 | \nabla_{\theta_i}L_i (\theta_i) = \mathbb{E}_{s,a \sim \rho(\cdot); s' \sim \mathcal(E)} [(r + \gamma \max_{a'} Q (s', a'; \theta_{i-1}) - Q(s,a; \theta_i)) \nabla_{\theta_i} Q(s,a; \theta_i)] 221 | \label{eq:gradientloss} 222 | \end{equation} 223 | 224 | The loss function is then minimized by either using stochastic gradient descent or more sophisticated methods like RMSprop. The behavior policy is $\epsilon$-greedy for ensuring sufficient exploration. 225 | \medskip 226 | 227 | \indent What makes the algorithm work is a technique known as \textit{experience replay}\cite{schaul2015prioritized}, by which we store the agent's experiences (also referred to as transitions) at each time-step, $e_t = (s_t, a_t, r_t, s_{t+1})$, in a data set $ \mathcal{D} = (e_1, ..., e_N)$, pooled over many episodes into a \textit{replay memory}. In the inner loop of our algorithm we apply Q-Learning updates, or mini-batch updates, to samples of experience, $e \sim \mathcal{D}$, picked up randomly from the pool of stored samples. After performing experience replay, the agent executes an action according to an $\epsilon$-greedy policy. Deep Q-Learning with experience replay is written in pseudo-code in Algorithm \ref{alg:DQN}. 228 | \begin{algorithm}[h] 229 | \caption{Deep Q-Learning with Experience Replay} 230 | \label{alg:DQN} 231 | \SetAlgoLined 232 | \DontPrintSemicolon 233 | Initialize replay memory $\mathcal{D}$ \; 234 | Initialize action value function Q with random weights \; 235 | \Repeat{terminated}{ 236 | Observe initial state $s_1$\; 237 | \For{t=1: T}{ 238 | Select an action $a_1$ using policy derived from Q (e.g. $\epsilon$-greedy)\; 239 | Carry out action $a_t$\; 240 | Observe reward $r_t$ and new state $s_{t+1}$\; 241 | Store transition $(s_t, a_t, r_t, s_{t+1})$ in replay buffer $\mathcal{D}$\; 242 | Sample random transitions $(s_j, a_j, r_j, s_{j+1})$ from $\mathcal{D}$\; 243 | Calculate target for each transition \; 244 | % MATCH SYNTAXXX!! LIKE s' 245 | 246 | \begin{equation} 247 | \text{Set } y_i = \begin{cases} 248 | r_j & \text{if } s_{j+1} \text{ is terminal}\\ 249 | r_j + \gamma \max_{a'} Q(s_{j+1},a';\theta) & \text{if } s_{j+1} \text{ is non-terminal} 250 | \end{cases} 251 | \end{equation} 252 | 253 | Train the Q network on $(y_j - Q(s_j, a_j; \theta))^2$ using Equation \ref{eq:gradientloss} 254 | } 255 | } 256 | \end{algorithm} 257 | 258 | The following is the Python code for the experience replay, which is of paramount importance for decoupling time-dependent transitions which would introduce a bias in the system: 259 | \begin{minted}{python} 260 | class ReplayMemory(object): 261 | """Replay Memory class for storing system's trajectories""" 262 | def __init__(self, capacity): 263 | self.capacity = capacity 264 | self.memory = [] 265 | self.position = 0 266 | 267 | def push(self, *args): 268 | """Saves a transition.""" 269 | if len(self.memory) < self.capacity: 270 | self.memory.append(None) # if we haven't reached full 271 | # capacity, we append a new transition 272 | self.memory[self.position] = Transition(*args) 273 | self.position = (self.position + 1) % self.capacity # e.g if the capacity 274 | # is 100, and our position is now 101, we don't append to position 101 275 | # (impossible), but to position 1 (its remainder), overwriting old data 276 | 277 | def sample(self, batch_size): 278 | return random.sample(self.memory, batch_size) 279 | 280 | def __len__(self): 281 | return len(self.memory) 282 | \end{minted} 283 | Deep Q-Learning has several advantages by using experience replay. Firstly, since each step of experience is potentially used in many weight updates, we have a greater data efficiency. Secondly, randomizing the samples allows for improved efficiency and reduces the updates variance, given that learning directly from consecutive samples of experience is inefficient due to the strong correlations between the samples. Thirdly, by learning off-policy we may be able to avoid dangerous unwanted feedback loops. For example, if we did train on-policy, if the maximizing action were to move on the left then the training samples would be dominated by samples from the left-hand side; if the maximizing action were the opposite one on the right, the same would happen with the right-hand side samples. This behavior could lead to unwanted outcomes, like getting stuck in a poor local minimum, or even catastrophically diverge. Thus, by using the off-policy experience replay we are able to smooth out learning and to avoid oscillation or divergence in the parameters. 284 | 285 | 286 | 287 | \\ 288 | The exploration and exploitation problem is dealt with by the use of the following $\varepsilon_{threshold}$, which decays over time; a lower threshold will result in higher exploitation of the learned optimal known actions: 289 | 290 | \begin{equation} 291 | \varepsilon_{threshold} = \varepsilon_{final} + (\varepsilon_{initial}-\varepsilon_{final})e^{-t/\varepsilon_{decay}} 292 | \end{equation} 293 | 294 | % \indent As regard the other two parameters, the \textit{kernel size} is the size of the square filter actuating convolution over the inputs (i.e. in our implementation we have a 5x5 filter). The second parameter, the \textit{stride}, is the number of pixels which are "skipped" each time while making the filter convolve. A higher stride will make the model less precise, but slower in learning; a $stride = 2$ is usually chosen because has been empirically proven to be the best choice for CNNs. 295 | 296 | 297 | \section{Towards Vision-Based Control} 298 | 299 | The first steps in trying to solve the inverted pendulum problem with raw pixels were based on a first implementation from Adam Paszke\footnote{\href{https://pytorch.org/tutorials/intermediate/reinforcement_q_learning.html}{Source: pytorch.org}}. The algorithm is based on Convolutional Neural Networks for predicting Q-values and implements basically the same structure of DQN.\\ 300 | Although this implementation was showing improvements in training, no matter how much training the system received, the mean reward was always swinging up and down and showing no sign of convergence or divergence. In particular, after some tenths of episodes showing an abrupt improvement in performance there were several episodes in which the agent "forgot" about the previous experiences, suddenly decreasing the performance. The problem that needs to be solved is the overfitting of the Convolutional Neural Network, which overestimated the state-action values leading to a sub-optimal policy. 301 | 302 | \subsection{Dealing with Overfitting} 303 | 304 | % As regards the overfitting problem there are a couple of tweaks to prevent it from happening at all. First of all, we implement a \textit{Dropout}\footnote{Dropout\cite{srivastava2014dropout} is a method by which some neural network neurons are switched off during training with a probability $p_i$, hence "dropped-out". During the testing phase, all the neurons are switched on with their output multiplied by a weight $p_i$. This method has proven to make neural networks more stable and robust.} regularization for improving the network stability. However, this has little effect in the training process, because of the intrinsic problem of learning, forgetting and learning again. 305 | \paragraph{Improving Image Pre-Processing} 306 | One first steps of state observation improvement implies simplifying the network by feeding it with a grayscale as input, thus reducing by one third the input dimensionality. Besides, the use of image subtraction used in the initial implementation could not capture some states; indeed, a better way to deal with changing environments over time is to feed the neural network a batch of images, them being the last N frames. This way, the state keeps track of past behaviors. By considering at least the last $N=2$ frames, velocity features can be extracted by the neural network from the image state. 307 | 308 | \begin{figure}[h!] 309 | \label{fig:ExampleExtractScreen} 310 | \centering 311 | \includegraphics[width=10cm]{images/example_extracted_screen.png} 312 | \caption[Pre-processed image of the environment]{Extracted screen from the inverted pendulum environment: the image is extracted by cropping, downsampling and applying grayscaling} 313 | \end{figure} 314 | 315 | \paragraph{Early Stopping} 316 | Thus, another method we can use is that of the \textit{Early Stopping}: in order to prevent overfitting, the agent is trained up to a point in which it has learned optimal behavior; from that point onward it would start behaving worse and worse and then restarting learning from scratch. We can detect this optimal situation by inserting a score threshold: when the mean of the last $K$ episodes overcome this threshold $\xi$, we stop the neural networks optimization. We have empirically set these two new hyper-parameters, which can be tweaked, to $K = 20$ and $\xi= 142$.\\ 317 | 318 | \paragraph{Reward Function Design} 319 | The reward function design is one of the most important aspects in Reinforcement Learning and can make the difference between an agent not training at all and one able to achieve super-human performance. Instead of the usual reward function from OpenAI Gym, we can build a new one being able to better give a feedback on our agent's decisions: 320 | 321 | \begin{equation} 322 | \label{eq:reward} 323 | \begin{aligned} 324 | r_1 = \frac{x_{max} - |x|}{x_{max}} - 0.8 \\ 325 | r_2 = \frac{\theta_{max} - |\theta|}{\theta_{max}} - 0.5 \\ 326 | r_{tot} = r_1 + r_2 327 | \end{aligned} 328 | \end{equation} 329 | However, in this case the reward function just has a minor impact on the overall performance, so we may as well use one which doesn't explicitly employ the state variables. 330 | 331 | \section{Final Model} 332 | \begin{table}[h!] 333 | \centering 334 | \begin{tabular}{ |p{4cm}|p{3cm}|p{2cm}|p{1.5cm}|p{1.2cm}| } 335 | \hline 336 | \multicolumn{5}{|c|}{Parameters} \\ 337 | \hline 338 | Layer & Number of Filters/Neurons & Activation & Kernel Size & Stride \\ 339 | \hline 340 | Convolutional Layer 1 & 64 & ReLu & 5 & 2\\ 341 | \hline 342 | Convolutional Layer 2 & 64 & ReLu & 5 & 2 \\ 343 | \hline 344 | Convolutional Layer 3 & 32 & ReLu & 5 & 2 \\ 345 | \hline 346 | Linear Output Layer & 1792 & None & - & - \\ 347 | \hline 348 | \end{tabular} 349 | \label{table:NeuralNetwork} 350 | \caption{Convolutional Neural Network hyper-parameters} 351 | \end{table} 352 | 353 | After improving the model with the aforementioned techniques, we obtain the following Convolutional Neural Network described in Table \ref{table:NeuralNetwork}. As regards the loss function and optimizer, we use: 354 | \begin{itemize} 355 | \item Loss Function: \textit{Huber loss function}, which is: 356 | \begin{equation} 357 | L(Q_{target}, Q_{predicted}) = \frac{1}{2}(Q_{target}-Q_{predicted})^2 358 | \end{equation} 359 | \item Optimizer: \textit{RMSprop}, which is able to do a gradient descent of the error in almost the most optimal path 360 | \end{itemize} 361 | 362 | The Python code for the DQN is the following; it takes a sequence of images as input and outputs the value function corresponding to each action: 363 | \begin{minted}{python} 364 | class DQN(nn.Module): 365 | """Convolutional Neural Network predicting the state-action values""" 366 | def __init__(self, h, w, outputs): 367 | super(DQN, self).__init__() 368 | self.conv1 = nn.Conv2d(nn_inputs, HIDDEN_LAYER_1, 369 | kernel_size=KERNEL_SIZE, stride=STRIDE) 370 | self.bn1 = nn.BatchNorm2d(HIDDEN_LAYER_1) 371 | self.conv2 = nn.Conv2d(HIDDEN_LAYER_1, HIDDEN_LAYER_2, 372 | kernel_size=KERNEL_SIZE, stride=STRIDE) 373 | self.bn2 = nn.BatchNorm2d(HIDDEN_LAYER_2) 374 | self.conv3 = nn.Conv2d(HIDDEN_LAYER_2, HIDDEN_LAYER_3, 375 | kernel_size=KERNEL_SIZE, stride=STRIDE) 376 | self.bn3 = nn.BatchNorm2d(HIDDEN_LAYER_3) 377 | 378 | # Number of Linear input connections depends on output of conv2d layers 379 | # and therefore the input image size, so compute it. 380 | def conv2d_size_out(size, kernel_size = KERNEL_SIZE, stride = STRIDE): 381 | return (size - (kernel_size - 1) - 1) // stride + 1 382 | 383 | convw = conv2d_size_out(conv2d_size_out(conv2d_size_out(w))) 384 | convh = conv2d_size_out(conv2d_size_out(conv2d_size_out(h))) 385 | linear_input_size = convw * convh * 32 386 | nn.Dropout() # Adds further regularization 387 | self.head = nn.Linear(linear_input_size, outputs) 388 | 389 | def forward(self, x): 390 | """Forward pass in the network""" 391 | x = F.relu(self.bn1(self.conv1(x))) 392 | x = F.relu(self.bn2(self.conv2(x))) 393 | x = F.relu(self.bn3(self.conv3(x))) 394 | return self.head(x.view(x.size(0), -1)) 395 | \end{minted} 396 | 397 | 398 | \begin{figure} 399 | \centering 400 | \includegraphics[width=\linewidth]{architecture.png} 401 | \caption{Architecture of the DQN with a Convolutional Neural Network for approximating state-action values} 402 | \label{fig:architecture} 403 | \end{figure} 404 | 405 | The final architecture of the DQN is represented in \ref{fig:architecture}. The following table shows the main Hyper-Parameters, based on the DQN with Experience Replay and Target Network, which further improves the performance of the system: 406 | 407 | \begin{table}[h!] 408 | \centering 409 | \begin{tabular}{ |p{6cm}|p{6cm}| } 410 | \hline 411 | \multicolumn{2}{|c|}{Hyper-Parameters Values} \\ 412 | \hline 413 | Batch Size & 128 \\ 414 | \hline 415 | Batch of Frames Size & 2 \\ 416 | \hline 417 | Discount Rate $\gamma$ & 0.999 \\ 418 | \hline 419 | Initial $\varepsilon$ & 0.9 \\ 420 | \hline 421 | Final $\varepsilon$ & 0.01 \\ 422 | \hline 423 | $\varepsilon$-Decay & 5000 \\ 424 | \hline 425 | Early Stop $\xi$ & 142 \\ 426 | \hline 427 | Image Height (pixels) & 60 \\ 428 | \hline 429 | Image Width (pixels) & 135 \\ 430 | \hline 431 | Maximum Memory Size & 100000 \\ 432 | \hline 433 | Target Model Update $\tau$ & 50 \\ 434 | \hline 435 | 436 | \end{tabular} 437 | \label{table:hyperParameters} 438 | \caption{Reinforcement Learning hyper-parameters} 439 | \end{table} 440 | 441 | 442 | \subsection{Final Results} 443 | 444 | After several unsuccessful or partially successful tries, using a tweaked CNN architecture, regulated hyper-parameters and adjustments in image pre-processing, dealing with overfitting and reward function design, we finally come to the experimental results. 445 | \medskip 446 | \begin{figure} 447 | \centering 448 | \includegraphics[width=\linewidth]{plot_score.png} 449 | \caption{Final results: plot of the obtained averaged out of a pool of 6 training runs. The light blue lines represent the confidence interval obtained via mean $\pm$ standard deviation. Most of the runs are able to get to the desired score in $\sim$ 800 episodes} 450 | \label{fig:results} 451 | \end{figure} 452 | As shown in Figure \ref{fig:results}, the inverted pendulum system is able to stabilize to obtain the 200 score. As to the best of the author's knowledge, this result has not been obtained yet in the Cartpole-v0 environment with DQN and only raw visual input, mainly because of the absence of early stopping which prevents overfitting.\\ 453 | 454 | % \footnote{The algorithm can be found at this \href{https://github.com/fedebberto/Vision_Based_CartPole_DQN}{Federico Berto's Github repository}.} 455 | 456 | \section{Potential Improvements and Future Work} 457 | Reinforcement Learning is fast-paced research area and it is even difficult at times to catch up with the latest trends. Regarding the control systems in particular, algorithms such as the LQR and MPCs still offer better performance and, most of all, theoretical guarantees on stability, at the cost of needing more information on the state and/or model of the system. \\ 458 | As we can also notice from the results, even though there is a confidence baseline for the stabilization score, the system is still prone to disturbances and inherent instabilities of the control policy and the neural network approximating the state-action values. One research direction would be to look for robust formulations of the problem \cite{DBLP:journals/corr/PintoDSG17}. Another interesting area, which has more technical guarantees on convergence and more efficient sampling of the state-space is the \textit{Model-Based} Reinforcement Learning \cite{DBLP:journals/corr/abs-1903-00374}, although it inherently needs a description via a model, thus renouncing the \textit{model-free} paradigm. Perhaps, the most interesting research direction is the combination of Reinforcement Learning and/or Optimal Control with Neural Ordinary Differential Equations \cite{NEURIPS2018_69386f6b}, a new class of Neural Networks which, thanks to their inherent capability to deal with differential equations, are revolutionizing the area of approximation and optimization of complex dynamical systems. 459 | 460 | \section{Conclusion} 461 | The goal of this report was to find a controller in a situation where state variables were not available, in particular by using only raw images to generate a control policy. 462 | The test benchmark we used is the inverted pendulum, which is used frequently to test non-linear controllers, which we used by extracting the necessary state information automatically thanks to the Deep Q-Learning, a Deep Reinforcement Learning algorithm capable of controlling agents with complex state-action spaces.\\ 463 | After implementing several tweaks to existing algorithms, we were able to obtain a controller capable of successfully obtaining the maximum reward score in the simulation by using Convolutional Neural Networks for choosing the optimal action leading to the optimal cumulative reward. The successful stabilization of the inverted pendulum shows that Reinforcement Learning is indeed capable of achieving good performances even with diffucult tasks.\\ 464 | Possible future developments include the implementation of new frameworks, such as Neural Ordinary Differential Equations, possibly paving the way to a better synergy of Reinforcement Learning and Optimal Control. 465 | \printbibliography 466 | \end{document} -------------------------------------------------------------------------------- /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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"Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------