def q_learning(env, estimator, num_episodes, discount_factor=1.0, epsilon=0.1, epsilon_decay=1.0):
"""
Q-Learning algorithm for off-policy TD control using Function Approximation.
Finds the optimal greedy policy while following an epsilon-greedy policy.
Args:
env: OpenAI environment.
estimator: Action-Value function estimator
num_episodes: Number of episodes to run for.
discount_factor: Gamma discount factor.
epsilon: Chance the sample a random action. Float betwen 0 and 1.
epsilon_decay: Each episode, epsilon is decayed by this factor
Returns:
An EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.
"""
# Keeps track of useful statistics
stats = plots.EpisodeStats(
episode_lengths=np.zeros(num_episodes),
episode_rewards=np.zeros(num_episodes))
for i_episode in range(num_episodes):
# The policy we're following
policy = make_epsilon_greedy_policy(
estimator, epsilon * epsilon_decay**i_episode, env.action_space.n)
# Print out which episode we're on, useful for debugging.
# Also print reward for last episode
last_reward = stats.episode_rewards[i_episode - 1]
sys.stdout.flush()
state = env.reset()
for t in itertools.count():
# sample action
action_probs = policy(state)
action = np.random.choice(np.arange(len(action_probs)),
p=action_probs)
next_state, reward, is_done, _ = env.step(action)
# Update statistics
stats.episode_rewards[i_episode] += reward
stats.episode_lengths[i_episode] = t
q_values_next = estimator.predict(next_state)
td_target = reward + discount_factor * np.max(q_values_next)
estimator.update(state, action, td_target)
print("\rStep {} @ Episode {}/{} ({})".format(t, i_episode + 1, num_episodes, last_reward), end="")
if is_done:
break
state = next_state
return stats
def n_step_sarsa(env,
num_episodes,
n=5,
discount_factor=1.0,
alpha=0.5,
epsilon=0.1):
"""
(n step)SARSA algorithm: On-policy TD control. Finds the optimal epsilon-greedy policy.
The algorithm looks forward n steps and then bootstraps from there to update the Q values.
Args:
env: OpenAI environment.
num_episodes: Number of episodes to run for.
n: future time steps to look ahead and calculate return for.
discount_factor: Gamma discount factor.
alpha: TD learning rate.
epsilon: Chance the sample a random action. Float betwen 0 and 1.
Returns:
A tuple (Q, stats).
Q is the optimal action-value function, a dictionary mapping state -> action values.
stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.
NOTE: some parts taken from https://github.com/Breakend/MultiStepBootstrappingInRL/blob/master/n_step_sarsa.py
"""
# The final action-value function.
# A nested dictionary that maps state -> (action -> action-value).
Q = defaultdict(lambda: np.zeros(env.action_space.n))
# Keeps track of useful statistics
stats = plots.EpisodeStats(episode_lengths=np.zeros(num_episodes),
episode_rewards=np.zeros(num_episodes))
# The policy we're following
policy = create_epsilon_greedy_policy(Q, epsilon, env.action_space.n)
for i_episode in range(num_episodes):
# Print out which episode we're on, useful for debugging.
if (i_episode + 1) % 10 == 0:
print("\rEpisode {}/{}.".format(i_episode + 1, num_episodes),
end="")
sys.stdout.flush()
# initializations
T = sys.maxsize
tau = 0
t = -1
stored_actions = {}
stored_rewards = {}
stored_states = {}
# initialize first state
state = env.reset()
action_probs = policy(state)
action = np.random.choice(env.action_space.n, p=action_probs)
stored_actions[0] = action
stored_states[0] = state
while tau < (T - 1):
t += 1
if t < T:
state, reward, done, _ = env.step(action)
stored_rewards[(t + 1) % (n + 1)] = reward
stored_states[(t + 1) % (n + 1)] = state
# Update statistics
stats.episode_rewards[i_episode] += reward
stats.episode_lengths[i_episode] = t
if done:
T = t + 1
else:
next_action_probs = policy(state)
action = np.random.choice(env.action_space.n,
p=next_action_probs)
stored_actions[(t + 1) % (n + 1)] = action
tau = t - n + 1
if tau >= 0:
# calculate G(tau:tau+n)
G = np.sum([
discount_factor**(i - tau - 1) * stored_rewards[i %
(n + 1)]
for i in range(tau + 1,
min(tau + n, T) + 1)
])
if tau + n < T:
G += discount_factor**n * Q[stored_states[
(tau + n) % (n + 1)]][stored_actions[(tau + n) %
(n + 1)]]
tau_s, tau_a = stored_states[tau %
(n + 1)], stored_actions[tau %
(n + 1)]
# update Q value with n step return
Q[tau_s][tau_a] += alpha * (G - Q[tau_s][tau_a])
return Q, stats
def sarsa_lambd(env, num_episodes, discount_factor=1.0, alpha=0.5, epsilon=0.1, lambd=0.9):
"""
SARSA algorithm: On-policy TD control. Finds the optimal epsilon-greedy policy.
Args:
env: OpenAI environment.
num_episodes: Number of episodes to run for.
discount_factor: Gamma discount factor.
alpha: TD learning rate.
epsilon: Chance the sample a random action. Float betwen 0 and 1.
Returns:
A tuple (Q, stats).
Q is the optimal action-value function, a dictionary mapping state -> action values.
stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.
"""
nA = env.action_space.n
# The final action-value function.
# A nested dictionary that maps state -> (action -> action-value).
Q = defaultdict(lambda: np.zeros(env.action_space.n))
# Keeps track of useful statistics
stats = plots.EpisodeStats(
episode_lengths=np.zeros(num_episodes),
episode_rewards=np.zeros(num_episodes))
# The policy we're following
policy = create_epsilon_greedy_policy(Q, epsilon, env.action_space.n)
for i_episode in range(num_episodes):
# Print out which episode we're on, useful for debugging.
if (i_episode + 1) % 100 == 0:
print("\rEpisode {}/{}.".format(i_episode + 1, num_episodes), end="")
sys.stdout.flush()
E = defaultdict(lambda: np.zeros(env.action_space.n))
state = env.reset()
action_probs = policy(state)
action = np.random.choice(env.action_space.n, p=action_probs)
for t in itertools.count():
# environment efforts after taking action
next_state, reward, done, _ = env.step(action)
next_action_probs = policy(next_state)
next_action = np.random.choice(env.action_space.n, p=next_action_probs)
# Update statistics
stats.episode_rewards[i_episode] += reward
stats.episode_lengths[i_episode] = t
td_error = reward + (discount_factor * Q[next_state][next_action]) - Q[state][action]
E[state][action] += 1
for s, _ in Q.items():
for a_ in range(nA):
Q[s][a_] += alpha * td_error * E[s][a_]
E[s][a_] *= discount_factor * lambd
if done:
break
state = next_state
action = next_action
return Q, stats
def n_step_expected_sarsa(env, num_episodes, n=10, gamma=0.9, alpha=0.1, epsilon=0.3):
"""
n step Expected SARSA algorithm: Off-policy TD control. Finds the optimal target policy.
Args:
env: OpenAI environment.
num_episodes: Number of episodes to run for.
n: future time steps to look ahead and calculate return for.
gamma: Gamma discount factor.
alpha: TD learning rate.
epsilon: Chance the sample a random action. Float betwen 0 and 1.
Returns:
A tuple (Q, stats).
Q is the optimal action-value function, a dictionary mapping state -> action values.
stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.
NOTE: some parts taken from https://github.com/Breakend/MultiStepBootstrappingInRL/blob/master/n_step_sarsa.py
"""
# initializations
# number of actions
nA = env.action_space.n
# create Q dict. A nested dict that maps state-> action values
Q = defaultdict(lambda: np.zeros(nA))
# policy we are following which is more
# exploratory and less greedy
behavior_policy = create_behavior_policy(Q, nA)
# Policy we are learning. Less exploratory
# than behavior policy -> means more greedy.
target_policy = create_target_policy(Q, nA)
# Keeps track of useful statistics
stats = plots.EpisodeStats(
episode_lengths=np.zeros(num_episodes),
episode_rewards=np.zeros(num_episodes))
max_reward = 0
total_reward = 0
rewards_per_episode = []
q_variance = []
for i_episode in range(num_episodes):
# Print out which episode we're on, useful for debugging.
if (i_episode + 1) % 10 == 0:
print("\rEpisode {}/{}.".format(i_episode + 1, num_episodes), end="")
sys.stdout.flush()
T = sys.maxsize
tau = 0
t = -1
stored_actions = {}
stored_rewards = {}
stored_states = {}
# reset env to get initial state
state = env.reset()
# get action probs from behavior policy
action_probs = behavior_policy(state)
action = np.random.choice(np.arange(nA), p=action_probs)
stored_actions[0] = action
stored_states[0] = state
while tau < (T - 1):
t += 1
if t < T:
state, reward, done, _ = env.step(action)
# Update statistics
stats.episode_rewards[i_episode] += reward
stats.episode_lengths[i_episode] = t
stored_rewards[(t+1) % (n+1)] = reward
stored_states[(t+1) % (n+1)] = state
if done:
T = t + 1
else:
action_probs = behavior_policy(state)
action = np.random.choice(np.arange(nA), p=action_probs)
stored_actions[(t+1) % (n+1)] = action
tau = t - n + 1
if tau >= 0:
# calculate rho
rho = np.prod(
[target_policy(stored_states[i%(n+1)])[stored_actions[i%(n+1)]]/behavior_policy(stored_states[i%(n+1)])[stored_actions[i%(n+1)]] for i in range(tau+1, min(tau+n-1, T-1)+1)]
)
# calculate return
G = np.sum([(gamma**(i-tau-1))*stored_rewards[i%(n+1)] for i in range(tau+1, min(tau+n, T)+1)])
if tau+n < T:
expected_sarsa_update = np.sum(
[target_policy(stored_states[(tau+n) % (n+1)])[a] * Q[stored_states[(tau+n) % (n+1)]][a] for a in range(nA)]
)
G += (gamma**n) * expected_sarsa_update
s_tau, a_tau = stored_states[tau % (n+1)], stored_actions[tau % (n+1)]
td_error = G - Q[s_tau][a_tau]
Q[s_tau][a_tau] += alpha * rho * td_error
return Q, stats
def q_learning(env, num_episodes, discount_factor=1.0, alpha=0.5, epsilon=0.1):
"""
Q-Learning algorithm: Off-policy TD control. Finds the optimal greedy policy
while following an epsilon-greedy policy
Args:
env: OpenAI environment.
num_episodes: Number of episodes to run for.
discount_factor: Gamma discount factor.
alpha: TD learning rate.
epsilon: Chance to sample a random action. Float between 0 and 1.
Returns:
A tuple (Q, episode_lengths).
Q is the optimal action-value function, a dictionary mapping state -> action values.
stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.
"""
# The final action-value function.
# A nested dictionary that maps state -> (action -> action-value).
Q = defaultdict(lambda: np.zeros(env.action_space.n))
# Keeps track of useful statistics
stats = plots.EpisodeStats(episode_lengths=np.zeros(num_episodes),
episode_rewards=np.zeros(num_episodes))
# The policy we're following
policy = create_epsilon_greedy_policy(Q, epsilon, env.action_space.n)
for i_episode in range(num_episodes):
# Print out which episode we're on, useful for debugging.
if (i_episode + 1) % 100 == 0:
print("\rEpisode {}/{}.".format(i_episode + 1, num_episodes),
end="")
sys.stdout.flush()
state = env.reset()
for t in itertools.count():
# sample action from behavior policy
action_probs = policy(state)
action = np.random.choice(env.action_space.n, p=action_probs)
# take action and observe environment's effects
next_state, reward, done, _ = env.step(action)
# Update statistics
stats.episode_rewards[i_episode] += reward
stats.episode_lengths[i_episode] = t
# sample next action from target policy
next_action = np.argmax(Q[next_state])
td_target = reward + discount_factor * Q[next_state][next_action]
# update Q value
Q[state][action] += alpha * (td_target - Q[state][action])
if done:
break
state = next_state
return Q, stats
def train(self):
stats = plots.EpisodeStats(
episode_lengths=np.zeros(self.num_episodes),
episode_rewards=np.zeros(self.num_episodes))
Transition = namedtuple("Transition", ["state", "action", "reward", "next_state", "done"])
for i_episode in range(self.num_episodes):
state = env.reset()
trajectory = list()
for t in itertools.count():
# get action prediction
action_probs = self.policy_estimator.predict(state).detach().numpy()
# get action
action = np.random.choice(np.arange(len(action_probs)), p=action_probs)
# take step
next_state, reward, done, _ = env.step(action)
trajectory.append(Transition(state=state,
action=action,
reward=reward,
next_state=next_state,
done=done))
stats.episode_lengths[i_episode] = t
stats.episode_rewards[i_episode] += reward
# Print out which step we're on, useful for debugging.
print("\rStep {} @ Episode {}/{} ({})".format(
t, i_episode + 1, self.num_episodes, stats.episode_rewards[i_episode - 1]), end="")
sys.stdout.flush()
if done:
break
state = next_state
for t, transition in enumerate(trajectory):
# get total reward
total_return = sum(self.gamma**i * tr.reward for i, tr in enumerate(trajectory[t:]))
# get value_estimate
value_estimate = self.value_estimator.predict(transition.state).detach()
advantage = torch.FloatTensor([total_return]) - value_estimate
advantage = torch.FloatTensor([advantage])
# update value estimator
self.value_estimator.update(transition.state,
torch.FloatTensor([total_return]),
self.value_optimizer)
# update policy estimator
action = torch.LongTensor([transition.action])
self.policy_estimator.update(transition.state,
advantage,
action,
self.policy_optimizer)
return stats
def q_sigma(env, num_episodes, n=10, gamma=0.9, alpha=0.1):
"""
n step q sigma algorithm: Off policy TD control.
Args:
env: OpenAI environment.
num_episodes: Number of episodes to run for.
n: future time steps to look ahead and calculate return for.
gamma: Gamma discount factor.
alpha: TD learning rate.
epsilon: Chance the sample a random action. Float betwen 0 and 1.
Returns:
A tuple (Q, stats).
Q is the optimal action-value function, a dictionary mapping state -> action values.
stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.
"""
nA = env.action_space.n
# Create dict Q. A mapping from state to action values
Q = defaultdict(lambda: np.zeros(nA))
# policy we are following which is more
# exploratory and less greedy
behavior_policy = create_behavior_policy(Q, nA)
# Policy we are learning. Less exploratory
# than behavior policy -> means more greedy.
target_policy = create_target_policy(Q, nA)
# Keeps track of useful statistics
stats = plots.EpisodeStats(episode_lengths=np.zeros(num_episodes),
episode_rewards=np.zeros(num_episodes))
for i_episode in range(num_episodes):
if (i_episode + 1) % 100 == 0:
print("\rEpisode {}/{}".format(i_episode + 1, num_episodes),
end="")
sys.stdout.flush()
T = sys.maxsize
t = -1
tau = 0
stored_actions = {}
stored_states = {}
stored_rewards = {}
stored_rho = {}
stored_sigma = {}
state = env.reset()
action_probs = behavior_policy(state)
action = np.random.choice(np.arange(nA), p=action_probs)
sigma = get_sigma(nA, action)
rho = target_policy(state)[action] / action_probs[action]
# store selected params
stored_states[0] = state
stored_actions[0] = action
stored_rho[0] = rho
stored_sigma[0] = sigma
while tau < (T - 1):
t += 1
if t < T:
# take action and observe envronment's effect
state, reward, done, _ = env.step(action)
stored_states[(t + 1) % (n + 1)] = state
stored_rewards[(t + 1) % (n + 1)] = reward
stats.episode_lengths[i_episode] = t
stats.episode_rewards[i_episode] += reward
if done:
T = t + 1
else:
action_probs = behavior_policy(state)
action = np.random.choice(np.arange(nA), p=action_probs)
sigma = get_sigma(nA, action)
rho = target_policy(state)[action] / action_probs[action]
stored_actions[(t + 1) % (n + 1)] = action
stored_sigma[(t + 1) % (n + 1)] = sigma
stored_rho[(t + 1) % (n + 1)] = rho
# tau is the time whose estimate is being updated
tau = t - n + 1
if tau >= 0:
if t + 1 < T:
G = Q[stored_states[(t + 1) %
(n + 1)]][stored_actions[(t + 1) %
(n + 1)]]
for k in range(min(t + 1, T), tau, -1):
if k == T:
G = stored_rewards[T % (n + 1)]
else:
s_k = stored_states[k % (n + 1)]
a_k = stored_actions[k % (n + 1)]
r_k = stored_rewards[k % (n + 1)]
sigma_k = stored_sigma[k % (n + 1)]
rho_k = stored_rho[k % (n + 1)]
v_ = np.sum([(target_policy(s_k)[a]) * Q[s_k][a]
for a in range(nA)])
G = r_k + gamma * ((sigma_k * rho_k) +
((1 - sigma_k) *
(target_policy(s_k)[a_k]))) * (
G - Q[s_k][a_k]) + gamma * v_
s_tau, a_tau = stored_states[tau %
(n + 1)], stored_actions[tau %
(n + 1)]
td_error = G - Q[s_tau][a_tau]
Q[s_tau][a_tau] += alpha * td_error
return Q, stats
def n_step_tree_backup(env, num_episodes, n=10, gamma=0.9, alpha=0.1):
"""
n step Tree Backup algorithm: Off policy TD control.
Args:
env: OpenAI environment.
num_episodes: Number of episodes to run for.
n: future time steps to look ahead and calculate return for.
gamma: Gamma discount factor.
alpha: TD learning rate.
epsilon: Chance the sample a random action. Float betwen 0 and 1.
Returns:
A tuple (Q, stats).
Q is the optimal action-value function, a dictionary mapping state -> action values.
stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.
"""
nA = env.action_space.n
# Create dict Q. A mapping from state to action values
Q = defaultdict(lambda: np.zeros(nA))
# policy we are following which is more
# exploratory and less greedy
behavior_policy = create_behavior_policy(Q, nA)
# Policy we are learning. Less exploratory
# than behavior policy -> means more greedy.
target_policy = create_target_policy(Q, nA)
# Keeps track of useful statistics
stats = plots.EpisodeStats(episode_lengths=np.zeros(num_episodes),
episode_rewards=np.zeros(num_episodes))
for i_episode in range(num_episodes):
if (i_episode + 1) % 100 == 0:
print("\rEpisode {}/{}.".format(i_episode + 1, num_episodes),
end="")
sys.stdout.flush()
T = sys.maxsize
tau = 0
t = -1
stored_actions = {}
stored_rewards = {}
stored_states = {}
# reset env to get initial state
state = env.reset()
# get action probs from behavior policy
action_probs = behavior_policy(state)
action = np.random.choice(np.arange(nA), p=action_probs)
stored_actions[0] = action
stored_states[0] = state
while tau < (T - 1):
t += 1
if t < T:
# take action and observe effects of the environment
state, reward, done, _ = env.step(action)
stored_states[(t + 1) % (n + 1)] = state
stored_rewards[(t + 1) % (n + 1)] = reward
stats.episode_lengths[i_episode] = t
stats.episode_rewards[i_episode] += reward
if done:
T = t + 1
else:
action_probs = behavior_policy(state)
action = np.random.choice(np.arange(nA), p=action_probs)
stored_actions[(t + 1) % (n + 1)] = action
tau = t - n + 1
if tau >= 0:
if (t + 1) >= T:
G = stored_rewards[T % (n + 1)]
else:
# get s[t+1] from stored states
s_t1 = stored_states[(t + 1) % (n + 1)]
# calulate sum of the leaf actions
leaf_sum = np.sum([(target_policy(s_t1)[a]) * Q[s_t1][a]
for a in range(env.nA)])
G = stored_rewards[(t + 1) % (n + 1)] + gamma * leaf_sum
for k in range(min(t, T - 1), tau, -1):
# get kth action and state
s_k, a_k = stored_states[k %
(n + 1)], stored_actions[k %
(n + 1)]
a_probs = np.sum([
target_policy(s_k)[a] * Q[s_k][a] for a in range(nA)
if a != a_k
])
G = stored_rewards[k % (n + 1)] + gamma * (
a_probs + target_policy(s_k)[a_k] * G)
s_tau, a_tau = stored_states[tau %
(n + 1)], stored_actions[tau %
(n + 1)]
td_error = G - Q[s_tau][a_tau]
Q[s_tau][a_tau] += alpha * td_error
return Q, stats
def n_step_expected_sarsa(env,
num_episodes,
n=5,
gamma=0.9,
epsilon=0.1,
alpha=0.1):
"""
(n step)Expected SARSA: On policy TD control. Finds the optimal epsilon greedy policy. The
algorithm is same as n step SARSA except that its last element is the branch over all action
possibilities weighted by their probabilities under pi(policy we are following).
Args:
env: The OpenAI environment.
num_episodes: Number of episodes to run for.
n: future time steps to look ahead and calculate return for.
discount_factor: Gamma discount factor.
alpha: TD learning rate.
epsilon: Chance to sample a random action. Float betwen 0 and 1.
Returns:
A tuple (Q, state)
Q: A dict mapping state -> action values. Q is the optimal action-value
function, a dictionary mapping state -> action values.
stats: An EpisodeStats object with two numpy arrays for episode_lengths
and episode_rewards.
"""
nA = env.action_space.n
# The final action-value function.
# A nested dictionary that maps state -> (action -> action-value).
Q = defaultdict(lambda: np.zeros(nA))
# policy we are following
policy = create_epsilon_greedy_policy(Q, nA, epsilon)
# track useful stats to plot
stats = plots.EpisodeStats(
episode_lengths=np.zeros(num_episodes),
episode_rewards=np.zeros(num_episodes),
)
for i_episode in range(num_episodes):
# print the current episode for debugging
if (i_episode + 1) % 100 == 0:
print("\rEpisode {}/{}.".format(i_episode + 1, num_episodes),
end="")
sys.stdout.flush()
# initializations
stored_rewards = {}
stored_states = {}
stored_actions = {}
T = sys.maxsize
t = -1
tau = 0
# reset OpenAI env to get the initial state
state = env.reset()
# get action probabilities from the policy function
action_probs = policy(state)
# sample action according to the action probabilities
action = np.random.choice(np.arange(nA), p=action_probs)
# store current action and state
stored_actions[0] = action
stored_states[0] = state
while tau < (T - 1):
t += 1
if t < T:
# observe environments effects after taking sampled action
next_state, reward, done, _ = env.step(action)
# assign next_state to current state
state = next_state
stored_states[(t + 1) % (n + 1)] = state
stored_rewards[(t + 1) % (n + 1)] = reward
stats.episode_lengths[i_episode] = t
stats.episode_rewards[i_episode] += reward
if done:
T = t + 1
else:
# select and store action A[t+1]
action_probs = policy(state)
action = np.random.choice(np.arange(nA), p=action_probs)
stored_actions[(t + 1) % (n + 1)] = action
tau = t - n + 1
if tau >= 0:
# caluclate return
G = np.sum([
(gamma**(i - tau - 1)) * stored_rewards[i % (n + 1)]
for i in range(tau + 1,
min(tau + n, T) + 1)
])
# this step we calculate value of all action possibilities weighted
# by their probabilities under pi(policy we are following).
if tau + n < T:
exp_sarsa_update = np.sum([
policy(stored_states[(tau + n) % (n + 1)])[a] *
Q[stored_states[(tau + n) % (n + 1)]][a]
for a in range(nA)
])
G += (gamma**n) * exp_sarsa_update
# update Q value here
s_tau, a_tau = stored_states[tau %
(n + 1)], stored_actions[tau %
(n + 1)]
Q[s_tau][a_tau] += alpha * (G - Q[s_tau][a_tau])
return Q, stats