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import sys, os
if 'google.colab' in sys.modules and not os.path.exists('.setup_complete'):
!wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/spring20/setup_colab.sh -O- | bash
!touch .setup_complete
# This code creates a virtual display to draw game images on.
# It will have no effect if your machine has a monitor.
if type(os.environ.get("DISPLAY")) is not str or len(os.environ.get("DISPLAY")) == 0:
!bash ../xvfb start
os.environ['DISPLAY'] = ':1'
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import gym
import numpy as np
env = gym.make("Taxi-v3")
env.reset()
env.render()
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n_states = env.observation_space.n
n_actions = env.action_space.n
print("n_states=%i, n_actions=%i" % (n_states, n_actions))
This time our policy should be a probability distribution.
policy[s,a] = P(take action a | in state s)
Since we still use integer state and action representations, you can use a 2-dimensional array to represent the policy.
Please initialize the policy uniformly, that is, probabililities of all actions should be equal.
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def initialize_policy(n_states, n_actions):
<YOUR CODE: create an array to store action probabilities>
return policy
policy = initialize_policy(n_states, n_actions)
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assert type(policy) in (np.ndarray, np.matrix)
assert np.allclose(policy, 1./n_actions)
assert np.allclose(np.sum(policy, axis=1), 1)
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def generate_session(env, policy, t_max=10**4):
"""
Play game until end or for t_max ticks.
:param policy: an array of shape [n_states,n_actions] with action probabilities
:returns: list of states, list of actions and sum of rewards
"""
states, actions = [], []
total_reward = 0.
s = env.reset()
for t in range(t_max):
# Hint: you can use np.random.choice for sampling action
# https://numpy.org/doc/stable/reference/random/generated/numpy.random.choice.html
a = <YOUR CODE: sample action from policy>
new_s, r, done, info = env.step(a)
# Record information we just got from the environment.
states.append(s)
actions.append(a)
total_reward += r
s = new_s
if done:
break
return states, actions, total_reward
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s, a, r = generate_session(env, policy)
assert type(s) == type(a) == list
assert len(s) == len(a)
assert type(r) in [float, np.float]
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# let's see the initial reward distribution
import matplotlib.pyplot as plt
%matplotlib inline
sample_rewards = [generate_session(env, policy, t_max=1000)[-1] for _ in range(200)]
plt.hist(sample_rewards, bins=20)
plt.vlines([np.percentile(sample_rewards, 50)], [0], [100], label="50'th percentile", color='green')
plt.vlines([np.percentile(sample_rewards, 90)], [0], [100], label="90'th percentile", color='red')
plt.legend()
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def select_elites(states_batch, actions_batch, rewards_batch, percentile):
"""
Select states and actions from games that have rewards >= percentile
:param states_batch: list of lists of states, states_batch[session_i][t]
:param actions_batch: list of lists of actions, actions_batch[session_i][t]
:param rewards_batch: list of rewards, rewards_batch[session_i]
:returns: elite_states,elite_actions, both 1D lists of states and respective actions from elite sessions
Please return elite states and actions in their original order
[i.e. sorted by session number and timestep within session]
If you are confused, see examples below. Please don't assume that states are integers
(they will become different later).
"""
reward_threshold = <YOUR CODE: compute minimum reward for elite sessions. Hint: use np.percentile()>
elite_states = <YOUR CODE>
elite_actions = <YOUR CODE>
return elite_states, elite_actions
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states_batch = [
[1, 2, 3], # game1
[4, 2, 0, 2], # game2
[3, 1], # game3
]
actions_batch = [
[0, 2, 4], # game1
[3, 2, 0, 1], # game2
[3, 3], # game3
]
rewards_batch = [
3, # game1
4, # game2
5, # game3
]
test_result_0 = select_elites(states_batch, actions_batch, rewards_batch, percentile=0)
test_result_30 = select_elites(states_batch, actions_batch, rewards_batch, percentile=30)
test_result_90 = select_elites(states_batch, actions_batch, rewards_batch, percentile=90)
test_result_100 = select_elites(states_batch, actions_batch, rewards_batch, percentile=100)
assert np.all(test_result_0[0] == [1, 2, 3, 4, 2, 0, 2, 3, 1]) \
and np.all(test_result_0[1] == [0, 2, 4, 3, 2, 0, 1, 3, 3]), \
"For percentile 0 you should return all states and actions in chronological order"
assert np.all(test_result_30[0] == [4, 2, 0, 2, 3, 1]) and \
np.all(test_result_30[1] == [3, 2, 0, 1, 3, 3]), \
"For percentile 30 you should only select states/actions from two first"
assert np.all(test_result_90[0] == [3, 1]) and \
np.all(test_result_90[1] == [3, 3]), \
"For percentile 90 you should only select states/actions from one game"
assert np.all(test_result_100[0] == [3, 1]) and\
np.all(test_result_100[1] == [3, 3]), \
"Please make sure you use >=, not >. Also double-check how you compute percentile."
print("Ok!")
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def update_policy(elite_states, elite_actions):
"""
Given old policy and a list of elite states/actions from select_elites,
return new updated policy where each action probability is proportional to
policy[s_i,a_i] ~ #[occurences of si and ai in elite states/actions]
Don't forget to normalize policy to get valid probabilities and handle 0/0 case.
In case you never visited a state, set probabilities for all actions to 1./n_actions
:param elite_states: 1D list of states from elite sessions
:param elite_actions: 1D list of actions from elite sessions
"""
new_policy = np.zeros([n_states, n_actions])
<YOUR CODE: update probabilities for actions given elite states & actions>
# Don't forget to set 1/n_actions for all actions in unvisited states.
return new_policy
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elite_states = [1, 2, 3, 4, 2, 0, 2, 3, 1]
elite_actions = [0, 2, 4, 3, 2, 0, 1, 3, 3]
new_policy = update_policy(elite_states, elite_actions)
assert np.isfinite(new_policy).all(), \
"Your new policy contains NaNs or +-inf. Make sure you don't divide by zero."
assert np.all(new_policy >= 0), \
"Your new policy can't have negative action probabilities"
assert np.allclose(new_policy.sum(axis=-1), 1), \
"Your new policy should be a valid probability distribution over actions"
reference_answer = np.array([
[1., 0., 0., 0., 0.],
[0.5, 0., 0., 0.5, 0.],
[0., 0.33333333, 0.66666667, 0., 0.],
[0., 0., 0., 0.5, 0.5]])
assert np.allclose(new_policy[:4, :5], reference_answer)
print("Ok!")
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from IPython.display import clear_output
def show_progress(rewards_batch, log, percentile, reward_range=[-990, +10]):
"""
A convenience function that displays training progress.
No cool math here, just charts.
"""
mean_reward = np.mean(rewards_batch)
threshold = np.percentile(rewards_batch, percentile)
log.append([mean_reward, threshold])
plt.figure(figsize=[8, 4])
plt.subplot(1, 2, 1)
plt.plot(list(zip(*log))[0], label='Mean rewards')
plt.plot(list(zip(*log))[1], label='Reward thresholds')
plt.legend()
plt.grid()
plt.subplot(1, 2, 2)
plt.hist(rewards_batch, range=reward_range)
plt.vlines([np.percentile(rewards_batch, percentile)],
[0], [100], label="percentile", color='red')
plt.legend()
plt.grid()
clear_output(True)
print("mean reward = %.3f, threshold=%.3f" % (mean_reward, threshold))
plt.show()
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# reset policy just in case
policy = initialize_policy(n_states, n_actions)
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n_sessions = 250 # sample this many sessions
percentile = 50 # take this percent of session with highest rewards
learning_rate = 0.5 # how quickly the policy is updated, on a scale from 0 to 1
log = []
for i in range(100):
%time sessions = [ <YOUR CODE: generate a list of n_sessions new sessions> ]
states_batch, actions_batch, rewards_batch = zip(*sessions)
elite_states, elite_actions = <YOUR CODE: select elite states & actions>
new_policy = <YOUR CODE: compute new policy>
policy = learning_rate * new_policy + (1 - learning_rate) * policy
# display results on chart
show_progress(rewards_batch, log, percentile)
You may have noticed that the taxi problem quickly converges from less than -1000 to a near-optimal score and then descends back into -50/-100. This is in part because the environment has some innate randomness. Namely, the starting points of passenger/driver change from episode to episode.
In case CEM failed to learn how to win from one distinct starting point, it will simply discard it because no sessions from that starting point will make it into the "elites".
To mitigate that problem, you can either reduce the threshold for elite sessions (duct tape way) or change the way you evaluate strategy (theoretically correct way). For each starting state, you can sample an action randomly, and then evaluate this action by running several games starting from it and averaging the total reward. Choosing elite sessions with this kind of sampling (where each session's reward is counted as the average of the rewards of all sessions with the same starting state and action) should improve the performance of your policy.
Go to ./deep_crossentropy_method.ipynb for a more serious task