def advance(self, state: MdpState, t: int, a: Action,
agent: Agent) -> Tuple[MdpState, Reward]:
"""
Advance from the current state given an action, based on the current state's model probability distribution.
:param state: State to advance.
:param t: Current time step.
:param a: Action.
:param agent: Agent.
:return: 2-tuple of next state and next reward.
"""
# get next-state / reward tuples
s_prime_rewards = [
(s_prime, reward)
for s_prime in self.p_S_prime_R_given_S_A[state][a]
for reward in self.p_S_prime_R_given_S_A[state][a][s_prime]
if self.p_S_prime_R_given_S_A[state][a][s_prime][reward] > 0.0
]
# get probability of each tuple
probs = np.array([
self.p_S_prime_R_given_S_A[state][a][s_prime][reward]
for s_prime, reward in s_prime_rewards
])
# sample next state and reward
self.state, next_reward = sample_list_item(
x=s_prime_rewards, probs=probs, random_state=self.random_state)
return self.state, next_reward
def sample_next_state_and_reward(
self, state: MdpState, action: Action,
random_state: RandomState) -> Tuple[MdpState, float]:
"""
Sample the environment model.
:param state: State.
:param action: Action.
:param random_state: Random state.
:return: 2-tuple of next state and reward.
"""
# sample next state
next_state_count = self.state_action_next_state_count[state][action]
next_states = list(next_state_count.keys())
total_count = sum(next_state_count.values())
probs = np.array([
next_state_count[next_state] / total_count
for next_state in next_states
])
next_state = sample_list_item(next_states, probs, random_state)
# get average reward in next state
reward = self.state_reward_averager[next_state].get_value()
return next_state, reward
def __act__(self, t: int) -> Action:
"""
Sample a random action based on current preferences.
:param t: Time step.
:return: Action.
"""
return sample_list_item(self.most_recent_state.AA, self.Pr_A,
self.random_state)
def test_sample_list_item():
x = [1, 2, 3]
p = np.array([0.1, 0.3, 0.6])
rng = RandomState(12345)
x_samples = [sample_list_item(x, p, rng) for _ in range(10000)]
xs, cnts = np.unique(x_samples, return_counts=True)
x_cnt = {x: cnt for x, cnt in zip(xs, cnts)}
total = sum(x_cnt.values())
x_p = [x_cnt[x] / total for x in x]
assert_allclose(p, x_p, atol=0.01)
with pytest.raises(ValueError,
match='Expected cumulative probabilities to sum to 1'):
sample_list_item([1, 2, 3], np.array([0.2, 0.3, 0.4]), rng)
def sample_state(self, random_state: RandomState) -> MdpState:
"""
Sample a previously encountered state uniformly.
:param random_state: Random state.
:return: State.
"""
return sample_list_item(
list(self.state_action_next_state_count.keys()), None,
random_state)
def sample_action(self, state: MdpState,
random_state: RandomState) -> Action:
"""
Sample a previously encountered action in a given state uniformly.
:param state: State.
:param random_state: Random state.
:return: Action
"""
return sample_list_item(
list(self.state_action_next_state_count[state].keys()), None,
random_state)
def test_stochastic_environment_model():
random_state = RandomState(12345)
model = StochasticEnvironmentModel()
actions = [
Action(i)
for i in range(5)
]
states = [
State(i, actions)
for i in range(5)
]
for t in range(1000):
state = sample_list_item(states, None, random_state)
action = sample_list_item(state.AA, None, random_state)
next_state = sample_list_item(states, None, random_state)
reward = Reward(None, random_state.randint(10))
model.update(state, action, next_state, reward)
environment_sequence = []
for i in range(1000):
state = model.sample_state(random_state)
action = model.sample_action(state, random_state)
next_state, reward = model.sample_next_state_and_reward(state, action, random_state)
environment_sequence.append((next_state, reward))
# uncomment the following line and run test to update fixture
# with open(f'{os.path.dirname(__file__)}/fixtures/test_stochastic_environment_model.pickle', 'wb') as file:
# pickle.dump(environment_sequence, file)
with open(f'{os.path.dirname(__file__)}/fixtures/test_stochastic_environment_model.pickle', 'rb') as file:
environment_sequence_fixture = pickle.load(file)
assert environment_sequence == environment_sequence_fixture
def __act__(self, t: int) -> Action:
"""
Act stochastically according to the policy.
:param t: Time tick.
:return: Action.
"""
self.most_recent_state: MdpState
# sample action according to policy for most recent state
action_prob = self.pi[self.most_recent_state]
actions = list(action_prob.keys())
probs = np.array(list(action_prob.values()))
return sample_list_item(x=actions,
probs=probs,
random_state=self.random_state)
def evaluate_q_pi(
agent: ActionValueMdpAgent,
environment: MdpEnvironment,
num_episodes: int,
exploring_starts: bool,
update_upon_every_visit: bool,
off_policy_agent: ActionValueMdpAgent = None,
) -> Tuple[Set[MdpState], float]:
"""
Perform Monte Carlo evaluation of an agent's policy within an environment, returning state-action values. This
evaluation function operates over rewards obtained at the end of episodes, so it is only appropriate for episodic
tasks.
:param agent: Agent containing target policy to be optimized.
:param environment: Environment.
:param num_episodes: Number of episodes to execute.
:param exploring_starts: Whether or not to use exploring starts, forcing a random action in the first time step.
This maintains exploration in the first state; however, unless each state has some nonzero probability of being
selected as the first state, there is no assurance that all state-action pairs will be sampled. If the initial state
is deterministic, consider passing False here and shifting the burden of exploration to the improvement step with
a nonzero epsilon (see `rlai.gpi.improvement.improve_policy_with_q_pi`).
:param update_upon_every_visit: True to update each state-action pair upon each visit within an episode, or False to
update each state-action pair upon the first visit within an episode.
:param off_policy_agent: Agent containing behavioral policy used to generate learning episodes. To ensure that the
state-action value estimates converge to those of the target policy, the policy of the `off_policy_agent` must be
soft (i.e., have positive probability for all state-action pairs that have positive probabilities in the agent's
target policy).
:return: 2-tuple of (1) set of only those states that were evaluated, and (2) the average reward obtained per
episode.
"""
logging.info(f'Running Monte Carlo evaluation of q_pi for {num_episodes} episode(s).')
evaluated_states = set()
episode_generation_agent = agent if off_policy_agent is None else off_policy_agent
episode_reward_averager = IncrementalSampleAverager()
episodes_per_print = max(1, int(num_episodes * 0.05))
for episode_i in range(num_episodes):
# reset the environment for the new run (always use the agent we're learning about, as state identifiers come
# from it), and reset the episode generate agent accordingly.
state = environment.reset_for_new_run(agent)
episode_generation_agent.reset_for_new_run(state)
# simulate until episode termination, keeping a trace of state-action pairs and their immediate rewards, as well
# as the times of their first visits (only if we're doing first-visit evaluation).
t = 0
state_action_first_t = None if update_upon_every_visit else {}
t_state_action_reward = []
total_reward = 0.0
while not state.terminal and (environment.T is None or t < environment.T):
evaluated_states.add(state)
if exploring_starts and t == 0:
a = sample_list_item(state.AA, None, environment.random_state)
else:
a = episode_generation_agent.act(t)
state_a = (state, a)
# mark time step of first visit, if we're doing first-visit evaluation.
if state_action_first_t is not None and state_a not in state_action_first_t:
state_action_first_t[state_a] = t
next_state, next_reward = environment.advance(state, t, a, agent)
t_state_action_reward.append((t, state_a, next_reward))
total_reward += next_reward.r
state = next_state
t += 1
episode_generation_agent.sense(state, t)
# work backwards through the trace to calculate discounted returns. need to work backward in order for the value
# of g at each time step t to be properly discounted. here, w is the importance-sampling weight of the agent's
# (target) policy compared to the episode generation policy (behavior).
g = 0.0
w = 1.0
for t, state_a, reward in reversed(t_state_action_reward):
g = agent.gamma * g + reward.r
# if we're doing every-visit, or if the current time step was the first visit to the state-action, then g
# is the discounted sample value. add it to our average.
if state_action_first_t is None or state_action_first_t[state_a] == t:
state, a = state_a
agent.q_S_A.initialize(state=state, a=a, alpha=None, weighted=True)
# the following two lines work correctly for on- and off-policy learning. in the former case, the agent
# and episode policies are the same, which makes w always equal to 1 (i.e., q_S_A is unweighted...the
# on-policy case). in off-policy learning, w will be the importance-sampling weight.
agent.q_S_A[state][a].update(value=g, weight=w)
w *= agent.pi[state][a] / episode_generation_agent.pi[state][a]
# if the importance sampling weight becomes zero (allowing floating-point tolerance), then we're done,
# as all subsequent weighted updates (at earlier time steps) will be zero. this is the sense in which
# off-policy learning only learns from the "tails" of episodes in which all state-action pairs of the
# episode are also greedy with respect to the agent's policy.
if w < 0.00000001:
break
episode_reward_averager.update(total_reward)
episodes_finished = episode_i + 1
if episodes_finished % episodes_per_print == 0:
logging.info(f'Finished {episodes_finished} of {num_episodes} episode(s).')
logging.info(f'Completed evaluation. Average reward per episode: {episode_reward_averager.get_value()}')
return evaluated_states, episode_reward_averager.get_value()
def evaluate_v_pi(
agent: ActionValueMdpAgent,
environment: MdpEnvironment,
num_episodes: int
) -> Dict[MdpState, float]:
"""
Perform Monte Carlo evaluation of an agent's policy within an environment, returning state values. Uses a random
action on the first time step to maintain exploration (exploring starts). This evaluation approach is only
marginally useful in practice, as the state-value estimates require a model of the environmental dynamics (i.e.,
the transition-reward probability distribution) in order to be applied. See `evaluate_q_pi` in this module for a
more feature-rich and useful evaluation approach (i.e., state-action value estimation). This evaluation function
operates over rewards obtained at the end of episodes, so it is only appropriate for episodic tasks.
:param agent: Agent.
:param environment: Environment.
:param num_episodes: Number of episodes to execute.
:return: Dictionary of MDP states and their estimated values under the agent's policy.
"""
logging.info(f'Running Monte Carlo evaluation of v_pi for {num_episodes} episode(s).')
v_pi: Dict[MdpState, IncrementalSampleAverager] = {
terminal_state: IncrementalSampleAverager()
for terminal_state in environment.terminal_states
}
episodes_per_print = int(num_episodes * 0.05)
for episode_i in range(num_episodes):
# start the environment in a random state
state = environment.reset_for_new_run(agent)
agent.reset_for_new_run(state)
# simulate until episode termination, keeping a trace of states and their immediate rewards, as well as the
# times of their first visits.
t = 0
state_first_t = {}
t_state_reward = []
while not state.terminal and (environment.T is None or t < environment.T):
if state not in state_first_t:
state_first_t[state] = t
if t == 0:
a = sample_list_item(state.AA, None, environment.random_state)
else:
a = agent.act(t)
next_state, reward = environment.advance(state, t, a, agent)
t_state_reward.append((t, state, reward))
state = next_state
t += 1
agent.sense(state, t)
# work backwards through the trace to calculate discounted returns. need to work backward in order for the value
# of g at each time step t to be properly discounted.
g = 0
for t, state, reward in reversed(t_state_reward):
g = agent.gamma * g + reward.r
# if the current time step was the first visit to the state, then g is the discounted sample value. add it
# to our average.
if state_first_t[state] == t:
if state not in v_pi:
v_pi[state] = IncrementalSampleAverager()
v_pi[state].update(g)
episodes_finished = episode_i + 1
if episodes_finished % episodes_per_print == 0:
logging.info(f'Finished {episodes_finished} of {num_episodes} episode(s).')
return {
s: v_pi[s].get_value()
for s in v_pi
}
def get_bootstrapped_state_action_value(
state: MdpState, t: int, mode: Mode, agent: MdpAgent,
q_S_A: StateActionValueEstimator,
environment: MdpEnvironment) -> Tuple[float, Action]:
"""
Get the bootstrapped state-action value for a state, also returning the next action.
:param state: State.
:param t: Time step.
:param mode: Bootstrap mode.
:param agent: Agent.
:param q_S_A: Current state-action value estimates.
:param environment: Environment.
:return: 2-tuple of the state's bootstrapped state-action value and the next action.
"""
next_a = None
# if the state is terminal, then all q-values are zero.
if state.terminal:
bootstrapped_s_a_value = 0.0
else:
# EXPECTED_SARSA: get expected q-value based on current policy and q-value estimates
if mode == Mode.EXPECTED_SARSA:
bootstrapped_s_a_value = sum(
(agent.pi[state][a] if state in agent.pi else 1 /
len(state.AA)) * (q_S_A[state][a].get_value(
) if state in q_S_A and a in q_S_A[state] else 0.0)
for a in state.AA)
else:
# SARSA: agent determines the t-d target action as well as the episode's next action, which are the same
# (we're on-policy).
if mode == Mode.SARSA:
td_target_a = next_a = agent.act(t)
# Q-LEARNING: select the action with max q-value from the state. if no q-values are estimated, then select
# the action uniformly randomly.
elif mode == Mode.Q_LEARNING:
if state in q_S_A and len(q_S_A[state]) > 0:
td_target_a = max(
q_S_A[state],
key=lambda action: q_S_A[state][action].get_value())
else:
td_target_a = sample_list_item(
state.AA,
probs=None,
random_state=environment.random_state)
else: # pragma no cover
raise ValueError(f'Unknown TD mode: {mode}')
# get the state-action value if we have an estimate for it; otherwise, it's zero.
if state in q_S_A and td_target_a in q_S_A[state]:
bootstrapped_s_a_value = q_S_A[state][td_target_a].get_value()
else:
bootstrapped_s_a_value = 0.0
# if we're off-policy, then we won't yet have a next action. ask the agent for an action now.
if next_a is None:
next_a = agent.act(t)
return bootstrapped_s_a_value, next_a
def mock_input(prompt: str) -> str:
s = human.most_recent_state
selected_a = sample_list_item(s.AA,
probs=None,
random_state=random_state)
return selected_a.name