From 67ab18e3d72c407525a0871636634283b1cd9afb Mon Sep 17 00:00:00 2001 From: Till Zemann Date: Sun, 23 Oct 2022 12:43:13 +0200 Subject: [PATCH] Add a tutorial notebook for Blackjack-v1 (#64) --- .../img/tutorials/blackjack_AE_loop.jpg | Bin 0 -> 93991 bytes .../tutorials/blackjack_with_usable_ace.png | Bin 0 -> 124868 bytes .../blackjack_without_usable_ace.png | Bin 0 -> 128872 bytes docs/tutorials/blackjack_tutorial.py | 364 ++++++++++++++++++ 4 files changed, 364 insertions(+) create mode 100644 docs/_static/img/tutorials/blackjack_AE_loop.jpg create mode 100644 docs/_static/img/tutorials/blackjack_with_usable_ace.png create mode 100644 docs/_static/img/tutorials/blackjack_without_usable_ace.png create mode 100644 docs/tutorials/blackjack_tutorial.py diff --git a/docs/_static/img/tutorials/blackjack_AE_loop.jpg b/docs/_static/img/tutorials/blackjack_AE_loop.jpg new file mode 100644 index 0000000000000000000000000000000000000000..5fa7ebb6ab7757a7e5cf88cfebb4663a2530c89a GIT binary 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zhU{>|QCbYyN?W5p-5-s+t&FmS;?`jq1;cPN*`Z_xXPV1nU8! literal 0 HcmV?d00001 diff --git a/docs/tutorials/blackjack_tutorial.py b/docs/tutorials/blackjack_tutorial.py new file mode 100644 index 000000000..363d9af5a --- /dev/null +++ b/docs/tutorials/blackjack_tutorial.py @@ -0,0 +1,364 @@ +""" +Solving Blackjack with Q-Learning +================================= + +""" + + +# %% +# .. image:: /_static/img/tutorials/blackjack_AE_loop.jpg +# :width: 650 +# :alt: agent-environment-diagram +# +# In this tutorial, we’ll explore and solve the *Blackjack-v1* +# environment. +# +# **Blackjack** is one of the most popular casino card games that is also +# 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. +# +# **Objective**: To win, your card sum should be greater than than the +# dealers without exceeding 21. +# +# **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). +# + + +# %% +# Imports and Environment Setup +# ------------------------------ +# + +# Author: Till Zemann +# License: MIT License + +from collections import defaultdict + +import gym +import numpy as np +import seaborn as sns +from matplotlib import pyplot as plt +from matplotlib.patches import Patch + +# Let's start by creating the blackjack environment. +# Note: We are going to follow the rules from Sutton & Barto. +# Other versions of the game can be found below for you to experiment. + +env = gym.make("Blackjack-v1", sab=True) + + +# %% +# .. code:: py +# +# # Other possible environment configurations: +# +# env = gym.make('Blackjack-v1', natural=True, sab=False)`` +# +# env = gym.make('Blackjack-v1', natural=False, sab=False)`` +# + + +# %% +# Observing the environment +# ------------------------------ +# +# 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. +# + +# reset the environment to get the first observation +done = False +observation, info = env.reset() + +print(observation) + + +# %% +# Note that our observation is a 3-tuple consisting of 3 discrete values: +# +# - The players current sum +# - Value of the dealers face-up card +# - Boolean whether the player holds a usable ace (An ace is usable if it +# counts as 11 without busting) +# + + +# %% +# Executing an action +# ------------------------------ +# +# After receiving our first observation, we are only going to use the +# ``env.step(action)`` function to interact with the environment. This +# function takes an action as input and executes it in the environment. +# Because that action changes the state of the environment, it returns +# four useful variables to us. These are: +# +# - ``next_state``: This is the observation that the agent will receive +# after taking the action. +# - ``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. +# - ``truncated``: This is a boolean variable that also indicates whether +# the episode ended by early truncation. +# - ``info``: This is a dictionary that might contain additional +# information about the environment. +# +# The ``next_state``, ``reward``, and ``done`` 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 +# environment you can ignore it. For example in Atari environments the +# 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. +# + +# sample a random action from all valid actions +action = env.action_space.sample() + +# 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) + + +# %% +# 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 +# responds but the output won’t be useful for training (it might even be +# harmful if the agent learns on invalid data). +# + + +# %% +# Building an agent +# ------------------------------ +# +# 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 +# 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``. +# + + +class BlackjackAgent: + def __init__(self, lr=1e-3, epsilon=0.1, epsilon_decay=1e-4): + """ + Initialize an 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): + """ + Returns the best action with probability (1 - epsilon) + and 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() + + # with probability (1 - epsilon) act greedily (exploit) + else: + action = np.argmax(self.q_values[state]) + return action + + 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 decay_epsilon(self): + self.epsilon = self.epsilon - epsilon_decay + + +# %% +# To train the agent, we will let the agent play one episode (one complete +# game is called an episode) at a time and then update it’s Q-values after +# each episode. The agent will have to experience a lot of episodes to +# explore the environment sufficiently. +# +# Now we should be ready to build the training loop. +# + +# hyperparameters +learning_rate = 1e-3 +start_epsilon = 0.8 +n_episodes = 200_000 +epsilon_decay = start_epsilon / n_episodes # less exploration over time + +agent = BlackjackAgent( + lr=learning_rate, epsilon=start_epsilon, epsilon_decay=epsilon_decay +) + + +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 +# ------------------------------ +# + + +def create_grids(agent, usable_ace=False): + + # convert our state-action values to state values + # and build a policy dictionary that maps observations to actions + V = 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) + + X, Y = np.meshgrid( + np.arange(12, 22), np.arange(1, 11) # players count + ) # dealers face-up card + + # 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_grid = X, Y, Z + + # 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]) + ) + return value_grid, policy_grid + + +def create_plots(value_grid, policy_grid, title="N/A"): + + # create a new figure with 2 subplots (left: state values, right: policy) + X, Y, Z = 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") + 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_xlabel("Player sum") + ax1.set_ylabel("Dealer showing") + ax1.zaxis.set_rotate_label(False) + ax1.set_zlabel("Value", fontsize=14, rotation=90) + ax1.view_init(20, 220) + + # 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_xlabel("Player sum") + ax2.set_ylabel("Dealer showing") + ax2.set_xticklabels(range(12, 22)) + ax2.set_yticklabels(["A"] + list(range(2, 11)), fontsize=12) + + # add a legend + legend_elements = [ + Patch(facecolor="lightgreen", edgecolor="black", label="Hit"), + Patch(facecolor="grey", edgecolor="black", label="Stick"), + ] + ax2.legend(handles=legend_elements, bbox_to_anchor=(1.3, 1)) + return fig + + +# state values & policy with usable ace (ace counts as 11) +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 +# + +# state values & policy without usable ace (ace counts as 1) +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 +# +# It's good practice to call env.close() at the end of your script, +# so that any used resources by the environment will be closed. +# + +env.close() + + +# %% +# Hopefully this Tutorial helped you get a grip of how to interact with +# OpenAI-Gym environments and sets you on a journey to solve many more RL +# challenges. +# +# 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 +# 5.3) - this way you can compare your results directly to the book. +# +# Best of fun! +#