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zhU{>|QCbYyN?W5p-5-s+t&FmS;?`jq1;cPN*`Z_xXPV1nU8! diff --git a/docs/tutorials/blackjack_tutorial.py b/docs/tutorials/blackjack_tutorial.py index 363d9af5a..683f36a9b 100644 --- a/docs/tutorials/blackjack_tutorial.py +++ b/docs/tutorials/blackjack_tutorial.py @@ -4,7 +4,6 @@ Solving Blackjack with Q-Learning """ - # %% # .. image:: /_static/img/tutorials/blackjack_AE_loop.jpg # :width: 650 @@ -17,10 +16,15 @@ Solving Blackjack with Q-Learning # infamous for being beatable under certain conditions. This version of # the game uses an infinite deck (we draw the cards with replacement), so # counting cards won’t be a viable strategy in our simulated game. +# Full documentation can be found at https://gymnasium.farama.org/environments/toy_text/blackjack # -# **Objective**: To win, your card sum should be greater than than the +# **Objective**: To win, your card sum should be greater than the # dealers without exceeding 21. # +# **Actions**: Agents can pick between two actions: +# - stand (0): the player takes no more cards +# - hit (1): the player will be given another card, however the player could get over 21 and bust +# # **Approach**: To solve this environment by yourself, you can pick your # favorite discrete RL algorithm. The presented solution uses *Q-learning* # (a model-free RL algorithm). @@ -35,13 +39,17 @@ Solving Blackjack with Q-Learning # Author: Till Zemann # License: MIT License +from __future__ import annotations + from collections import defaultdict -import gym +import matplotlib.pyplot as plt import numpy as np import seaborn as sns -from matplotlib import pyplot as plt from matplotlib.patches import Patch +from tqdm import tqdm + +import gymnasium as gym # Let's start by creating the blackjack environment. # Note: We are going to follow the rules from Sutton & Barto. @@ -49,15 +57,16 @@ from matplotlib.patches import Patch env = gym.make("Blackjack-v1", sab=True) - # %% # .. code:: py # -# # Other possible environment configurations: +# # Other possible environment configurations are: # -# env = gym.make('Blackjack-v1', natural=True, sab=False)`` +# env = gym.make('Blackjack-v1', natural=True, sab=False) +# # Whether to give an additional reward for starting with a natural blackjack, i.e. starting with an ace and ten (sum is 21). # -# env = gym.make('Blackjack-v1', natural=False, sab=False)`` +# env = gym.make('Blackjack-v1', natural=False, sab=False) +# # Whether to follow the exact rules outlined in the book by Sutton and Barto. If `sab` is `True`, the keyword argument `natural` will be ignored. # @@ -68,21 +77,18 @@ env = gym.make("Blackjack-v1", sab=True) # First of all, we call ``env.reset()`` to start an episode. This function # resets the environment to a starting position and returns an initial # ``observation``. We usually also set ``done = False``. This variable -# will be useful later to check if a game is terminated. In this tutorial -# we will use the terms observation and state synonymously but in more -# complex problems a state might differ from the observation it is based -# on. +# will be useful later to check if a game is terminated (i.e., the player wins or loses). # # reset the environment to get the first observation done = False observation, info = env.reset() -print(observation) +# observation = (16, 9, False) # %% -# Note that our observation is a 3-tuple consisting of 3 discrete values: +# Note that our observation is a 3-tuple consisting of 3 values: # # - The players current sum # - Value of the dealers face-up card @@ -106,13 +112,13 @@ print(observation) # - ``reward``: This is the reward that the agent will receive after # taking the action. # - ``terminated``: This is a boolean variable that indicates whether or -# not the episode is over. +# not the environment has terminated. # - ``truncated``: This is a boolean variable that also indicates whether -# the episode ended by early truncation. +# the episode ended by early truncation, i.e., a time limit is reached. # - ``info``: This is a dictionary that might contain additional # information about the environment. # -# The ``next_state``, ``reward``, and ``done`` variables are +# The ``next_state``, ``reward``, ``terminated`` and ``truncated`` variables are # self-explanatory, but the ``info`` variable requires some additional # explanation. This variable contains a dictionary that might have some # extra information about the environment, but in the Blackjack-v1 @@ -120,34 +126,29 @@ print(observation) # info dictionary has a ``ale.lives`` key that tells us how many lives the # agent has left. If the agent has 0 lives, then the episode is over. # -# Blackjack-v1 doesn’t have a ``env.render()`` function to render the -# environment, but in other environments you can use this function to -# watch the agent play. Important to note is that using ``env.render()`` -# is optional - the environment is going to work even if you don’t render -# it, but it can be helpful to see an episode rendered out to get an idea -# of how the current policy behaves. Note that it is not a good idea to -# call this function in your training loop because rendering slows down -# training by a lot. Rather try to build an extra loop to evaluate and -# showcase the agent after training. +# Note that it is not a good idea to call ``env.render()`` in your training +# loop because rendering slows down training by a lot. Rather try to build +# an extra loop to evaluate and showcase the agent after training. # # sample a random action from all valid actions action = env.action_space.sample() +# action=1 # execute the action in our environment and receive infos from the environment observation, reward, terminated, truncated, info = env.step(action) -print("observation:", observation) -print("reward:", reward) -print("terminated:", terminated) -print("truncated:", truncated) -print("info:", info) +# observation=(24, 10, False) +# reward=-1.0 +# terminated=True +# truncated=False +# info={} # %% # Once ``terminated = True`` or ``truncated=True``, we should stop the # current episode and begin a new one with ``env.reset()``. If you -# continue executing act`ons without resetting the environment, it still +# continue executing actions without resetting the environment, it still # responds but the output won’t be useful for training (it might even be # harmful if the agent learns on invalid data). # @@ -159,7 +160,7 @@ print("info:", info) # # Let’s build a ``Q-learning agent`` to solve *Blackjack-v1*! We’ll need # some functions for picking an action and updating the agents action -# values. To ensure that the agents expores the environment, one possible +# values. To ensure that the agents explores the environment, one possible # solution is the ``epsilon-greedy`` strategy, where we pick a random # action with the percentage ``epsilon`` and the greedy action (currently # valued as the best) ``1 - epsilon``. @@ -167,43 +168,69 @@ print("info:", info) class BlackjackAgent: - def __init__(self, lr=1e-3, epsilon=0.1, epsilon_decay=1e-4): - """ - Initialize an Reinforcement Learning agent with an empty dictionary + def __init__( + self, + learning_rate: float, + initial_epsilon: float, + epsilon_decay: float, + final_epsilon: float, + discount_factor: float = 0.95, + ): + """Initialize a Reinforcement Learning agent with an empty dictionary of state-action values (q_values), a learning rate and an epsilon. - """ - self.q_values = defaultdict( - lambda: np.zeros(env.action_space.n) - ) # maps a state to action values - self.lr = lr - self.epsilon = epsilon - self.epsilon_decay = epsilon_decay - def get_action(self, state): + Args: + learning_rate: The learning rate + initial_epsilon: The initial epsilon value + epsilon_decay: The decay for epsilon + final_epsilon: The final epsilon value + discount_factor: The discount factor for computing the Q-value + """ + self.q_values = defaultdict(lambda: np.zeros(env.action_space.n)) + + self.lr = learning_rate + self.discount_factor = discount_factor + + self.epsilon = initial_epsilon + self.epsilon_decay = epsilon_decay + self.final_epsilon = final_epsilon + + self.training_error = [] + + def get_action(self, obs: tuple[int, int, bool]) -> int: """ Returns the best action with probability (1 - epsilon) - and a random action with probability epsilon to ensure exploration. + otherwise a random action with probability epsilon to ensure exploration. """ # with probability epsilon return a random action to explore the environment if np.random.random() < self.epsilon: - action = env.action_space.sample() + return env.action_space.sample() # with probability (1 - epsilon) act greedily (exploit) else: - action = np.argmax(self.q_values[state]) - return action + return int(np.argmax(self.q_values[obs])) - def update(self, state, action, reward, next_state, done): - """ - Updates the Q-value of an action. - """ - old_q_value = self.q_values[state][action] - max_future_q = np.max(self.q_values[next_state]) - target = reward + self.lr * max_future_q * (1 - done) - self.q_values[state][action] = (1 - self.lr) * old_q_value + self.lr * target + def update( + self, + obs: tuple[int, int, bool], + action: int, + reward: float, + terminated: bool, + next_obs: tuple[int, int, bool], + ): + """Updates the Q-value of an action.""" + future_q_value = (not terminated) * np.max(self.q_values[next_obs]) + temporal_difference = ( + reward + self.discount_factor * future_q_value - self.q_values[obs][action] + ) + + self.q_values[obs][action] = ( + self.q_values[obs][action] + self.lr * temporal_difference + ) + self.training_error.append(temporal_difference) def decay_epsilon(self): - self.epsilon = self.epsilon - epsilon_decay + self.epsilon = max(self.final_epsilon, self.epsilon - epsilon_decay) # %% @@ -216,89 +243,144 @@ class BlackjackAgent: # # hyperparameters -learning_rate = 1e-3 -start_epsilon = 0.8 -n_episodes = 200_000 -epsilon_decay = start_epsilon / n_episodes # less exploration over time +learning_rate = 0.01 +n_episodes = 100_000 +start_epsilon = 1.0 +epsilon_decay = start_epsilon / (n_episodes / 2) # reduce the exploration over time +final_epsilon = 0.1 agent = BlackjackAgent( - lr=learning_rate, epsilon=start_epsilon, epsilon_decay=epsilon_decay + learning_rate=learning_rate, + initial_epsilon=start_epsilon, + epsilon_decay=epsilon_decay, + final_epsilon=final_epsilon, ) - -def train(agent, n_episodes): - for episode in range(n_episodes): - - # reset the environment - state, info = env.reset() - done = False - - # play one episode - while not done: - action = agent.get_action(observation) - next_state, reward, terminated, truncated, info = env.step(action) - done = ( - terminated or truncated - ) # if the episode terminated or was truncated early, set done to True - agent.update(state, action, reward, next_state, done) - state = next_state - - agent.update(state, action, reward, next_state, done) - - # %% # Great, let’s train! # - -train(agent, n_episodes) - - -# %% -# Visualizing the results -# ------------------------------ +# Info: The current hyperparameters are set to quickly train a decent agent. +# If you want to converge to the optimal policy, try increasing +# the n_episodes by 10x and lower the learning_rate (e.g. to 0.001). # -def create_grids(agent, usable_ace=False): +env = gym.wrappers.RecordEpisodeStatistics(env, deque_size=n_episodes) +for episode in tqdm(range(n_episodes)): + obs, info = env.reset() + done = False + # play one episode + while not done: + action = agent.get_action(obs) + next_obs, reward, terminated, truncated, info = env.step(action) + + # update the agent + agent.update(obs, action, reward, terminated, next_obs) + + # update if the environment is done and the current obs + done = terminated or truncated + obs = next_obs + + agent.decay_epsilon() + + +# %% +# Visualizing the training +# ------------------------------ +# + +rolling_length = 500 +fig, axs = plt.subplots(ncols=3, figsize=(12, 5)) +axs[0].set_title("Episode rewards") +reward_moving_average = ( + np.convolve( + np.array(env.return_queue).flatten(), np.ones(rolling_length), mode="valid" + ) + / rolling_length +) +axs[0].plot(range(len(reward_moving_average)), reward_moving_average) +axs[1].set_title("Episode lengths") +length_moving_average = ( + np.convolve( + np.array(env.length_queue).flatten(), np.ones(rolling_length), mode="same" + ) + / rolling_length +) +axs[1].plot(range(len(length_moving_average)), length_moving_average) +axs[2].set_title("Training Error") +training_error_moving_average = ( + np.convolve(np.array(agent.training_error), np.ones(rolling_length), mode="same") + / rolling_length +) +axs[2].plot(range(len(training_error_moving_average)), training_error_moving_average) +plt.tight_layout() +plt.show() + +# %% +# .. image:: /_static/img/tutorials/blackjack_training_plots.png +# + + +# %% +# Visualising the policy +# ------------------------------ + + +def create_grids(agent, usable_ace=False): + """Create value and policy grid given an agent.""" # convert our state-action values to state values # and build a policy dictionary that maps observations to actions - V = defaultdict(float) + state_value = defaultdict(float) policy = defaultdict(int) for obs, action_values in agent.q_values.items(): - V[obs] = np.max(action_values) - policy[obs] = np.argmax(action_values) + state_value[obs] = float(np.max(action_values)) + policy[obs] = int(np.argmax(action_values)) - X, Y = np.meshgrid( - np.arange(12, 22), np.arange(1, 11) # players count - ) # dealers face-up card + player_count, dealer_count = np.meshgrid( + # players count, dealers face-up card + np.arange(12, 22), + np.arange(1, 11), + ) # create the value grid for plotting - Z = np.apply_along_axis( - lambda obs: V[(obs[0], obs[1], usable_ace)], axis=2, arr=np.dstack([X, Y]) + value = np.apply_along_axis( + lambda obs: state_value[(obs[0], obs[1], usable_ace)], + axis=2, + arr=np.dstack([player_count, dealer_count]), ) - value_grid = X, Y, Z + value_grid = player_count, dealer_count, value # create the policy grid for plotting policy_grid = np.apply_along_axis( - lambda obs: policy[(obs[0], obs[1], usable_ace)], axis=2, arr=np.dstack([X, Y]) + lambda obs: policy[(obs[0], obs[1], usable_ace)], + axis=2, + arr=np.dstack([player_count, dealer_count]), ) return value_grid, policy_grid -def create_plots(value_grid, policy_grid, title="N/A"): - +def create_plots(value_grid, policy_grid, title: str): + """Creates a plot using a value and policy grid.""" # create a new figure with 2 subplots (left: state values, right: policy) - X, Y, Z = value_grid + player_count, dealer_count, value = value_grid fig = plt.figure(figsize=plt.figaspect(0.4)) fig.suptitle(title, fontsize=16) # plot the state values ax1 = fig.add_subplot(1, 2, 1, projection="3d") - ax1.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap="viridis", edgecolor="none") + ax1.plot_surface( + player_count, + dealer_count, + value, + rstride=1, + cstride=1, + cmap="viridis", + edgecolor="none", + ) plt.xticks(range(12, 22), range(12, 22)) plt.yticks(range(1, 11), ["A"] + list(range(2, 11))) - ax1.set_title("State values: " + title) + ax1.set_title(f"State values: {title}") ax1.set_xlabel("Player sum") ax1.set_ylabel("Dealer showing") ax1.zaxis.set_rotate_label(False) @@ -308,7 +390,7 @@ def create_plots(value_grid, policy_grid, title="N/A"): # plot the policy fig.add_subplot(1, 2, 2) ax2 = sns.heatmap(policy_grid, linewidth=0, annot=True, cmap="Accent_r", cbar=False) - ax2.set_title("Policy: " + title) + ax2.set_title(f"Policy: {title}") ax2.set_xlabel("Player sum") ax2.set_ylabel("Dealer showing") ax2.set_xticklabels(range(12, 22)) @@ -328,7 +410,6 @@ value_grid, policy_grid = create_grids(agent, usable_ace=True) fig1 = create_plots(value_grid, policy_grid, title="With usable ace") plt.show() - # %% # .. image:: /_static/img/tutorials/blackjack_with_usable_ace.png # @@ -338,7 +419,6 @@ value_grid, policy_grid = create_grids(agent, usable_ace=False) fig2 = create_plots(value_grid, policy_grid, title="Without usable ace") plt.show() - # %% # .. image:: /_static/img/tutorials/blackjack_without_usable_ace.png # @@ -346,7 +426,12 @@ plt.show() # so that any used resources by the environment will be closed. # -env.close() +# %% +# Think you can do better? +# ------------------------------ + +# You can visualize the environment using the play function +# and try to win a few games. # %% @@ -357,7 +442,7 @@ env.close() # It is recommended that you solve this environment by yourself (project # based learning is really effective!). You can apply your favorite # discrete RL algorithm or give Monte Carlo ES a try (covered in `Sutton & -# Barto `__, section +# Barto `_, section # 5.3) - this way you can compare your results directly to the book. # # Best of fun!