from dataclasses import dataclass
from typing import Any, TypeVar, cast
import gymnasium as gym
import numpy as np
import torch
from tianshou.data import Batch
from tianshou.data.batch import BatchProtocol
from tianshou.data.types import ActBatchProtocol, ObsBatchProtocol, RolloutBatchProtocol
from tianshou.policy import BasePolicy
from tianshou.policy.base import TLearningRateScheduler, TrainingStats
[docs]
@dataclass(kw_only=True)
class PSRLTrainingStats(TrainingStats):
psrl_rew_mean: float = 0.0
psrl_rew_std: float = 0.0
TPSRLTrainingStats = TypeVar("TPSRLTrainingStats", bound=PSRLTrainingStats)
[docs]
class PSRLModel:
"""Implementation of Posterior Sampling Reinforcement Learning Model.
:param trans_count_prior: dirichlet prior (alphas), with shape
(n_state, n_action, n_state).
:param rew_mean_prior: means of the normal priors of rewards,
with shape (n_state, n_action).
:param rew_std_prior: standard deviations of the normal priors
of rewards, with shape (n_state, n_action).
:param discount_factor: in [0, 1].
:param epsilon: for precision control in value iteration.
:param lr_scheduler: a learning rate scheduler that adjusts the learning rate in
optimizer in each policy.update(). Default to None (no lr_scheduler).
"""
def __init__(
self,
trans_count_prior: np.ndarray,
rew_mean_prior: np.ndarray,
rew_std_prior: np.ndarray,
discount_factor: float,
epsilon: float,
) -> None:
self.trans_count = trans_count_prior
self.n_state, self.n_action = rew_mean_prior.shape
self.rew_mean = rew_mean_prior
self.rew_std = rew_std_prior
self.rew_square_sum = np.zeros_like(rew_mean_prior)
self.rew_std_prior = rew_std_prior
self.discount_factor = discount_factor
self.rew_count = np.full(rew_mean_prior.shape, epsilon) # no weight
self.eps = epsilon
self.policy: np.ndarray
self.value = np.zeros(self.n_state)
self.updated = False
self.__eps = np.finfo(np.float32).eps.item()
[docs]
def observe(
self,
trans_count: np.ndarray,
rew_sum: np.ndarray,
rew_square_sum: np.ndarray,
rew_count: np.ndarray,
) -> None:
"""Add data into memory pool.
For rewards, we have a normal prior at first. After we observed a
reward for a given state-action pair, we use the mean value of our
observations instead of the prior mean as the posterior mean. The
standard deviations are in inverse proportion to the number of the
corresponding observations.
:param trans_count: the number of observations, with shape
(n_state, n_action, n_state).
:param rew_sum: total rewards, with shape
(n_state, n_action).
:param rew_square_sum: total rewards' squares, with shape
(n_state, n_action).
:param rew_count: the number of rewards, with shape
(n_state, n_action).
"""
self.updated = False
self.trans_count += trans_count
sum_count = self.rew_count + rew_count
self.rew_mean = (self.rew_mean * self.rew_count + rew_sum) / sum_count
self.rew_square_sum += rew_square_sum
raw_std2 = self.rew_square_sum / sum_count - self.rew_mean**2
self.rew_std = np.sqrt(
1 / (sum_count / (raw_std2 + self.__eps) + 1 / self.rew_std_prior**2),
)
self.rew_count = sum_count
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def sample_trans_prob(self) -> np.ndarray:
return torch.distributions.Dirichlet(torch.from_numpy(self.trans_count)).sample().numpy()
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def sample_reward(self) -> np.ndarray:
return np.random.normal(self.rew_mean, self.rew_std)
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def solve_policy(self) -> None:
self.updated = True
self.policy, self.value = self.value_iteration(
self.sample_trans_prob(),
self.sample_reward(),
self.discount_factor,
self.eps,
self.value,
)
[docs]
@staticmethod
def value_iteration(
trans_prob: np.ndarray,
rew: np.ndarray,
discount_factor: float,
eps: float,
value: np.ndarray,
) -> tuple[np.ndarray, np.ndarray]:
"""Value iteration solver for MDPs.
:param trans_prob: transition probabilities, with shape
(n_state, n_action, n_state).
:param rew: rewards, with shape (n_state, n_action).
:param eps: for precision control.
:param discount_factor: in [0, 1].
:param value: the initialize value of value array, with
shape (n_state, ).
:return: the optimal policy with shape (n_state, ).
"""
Q = rew + discount_factor * trans_prob.dot(value)
new_value = Q.max(axis=1)
while not np.allclose(new_value, value, eps):
value = new_value
Q = rew + discount_factor * trans_prob.dot(value)
new_value = Q.max(axis=1)
# this is to make sure if Q(s, a1) == Q(s, a2) -> choose a1/a2 randomly
Q += eps * np.random.randn(*Q.shape)
return Q.argmax(axis=1), new_value
def __call__(
self,
obs: np.ndarray,
state: Any = None,
info: Any = None,
) -> np.ndarray:
if not self.updated:
self.solve_policy()
return self.policy[obs]
[docs]
class PSRLPolicy(BasePolicy[TPSRLTrainingStats]):
"""Implementation of Posterior Sampling Reinforcement Learning.
Reference: Strens M. A Bayesian framework for reinforcement learning [C]
//ICML. 2000, 2000: 943-950.
:param trans_count_prior: dirichlet prior (alphas), with shape
(n_state, n_action, n_state).
:param rew_mean_prior: means of the normal priors of rewards,
with shape (n_state, n_action).
:param rew_std_prior: standard deviations of the normal priors
of rewards, with shape (n_state, n_action).
:param action_space: Env's action_space.
:param discount_factor: in [0, 1].
:param epsilon: for precision control in value iteration.
:param add_done_loop: whether to add an extra self-loop for the
terminal state in MDP. Default to False.
:param observation_space: Env's observation space.
:param lr_scheduler: if not None, will be called in `policy.update()`.
.. seealso::
Please refer to :class:`~tianshou.policy.BasePolicy` for more detailed
explanation.
"""
def __init__(
self,
*,
trans_count_prior: np.ndarray,
rew_mean_prior: np.ndarray,
rew_std_prior: np.ndarray,
action_space: gym.spaces.Discrete,
discount_factor: float = 0.99,
epsilon: float = 0.01,
add_done_loop: bool = False,
observation_space: gym.Space | None = None,
lr_scheduler: TLearningRateScheduler | None = None,
) -> None:
super().__init__(
action_space=action_space,
observation_space=observation_space,
action_scaling=False,
action_bound_method=None,
lr_scheduler=lr_scheduler,
)
assert 0.0 <= discount_factor <= 1.0, "discount factor should be in [0, 1]"
self.model = PSRLModel(
trans_count_prior,
rew_mean_prior,
rew_std_prior,
discount_factor,
epsilon,
)
self._add_done_loop = add_done_loop
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def forward(
self,
batch: ObsBatchProtocol,
state: dict | BatchProtocol | np.ndarray | None = None,
**kwargs: Any,
) -> ActBatchProtocol:
"""Compute action over the given batch data with PSRL model.
:return: A :class:`~tianshou.data.Batch` with "act" key containing
the action.
.. seealso::
Please refer to :meth:`~tianshou.policy.BasePolicy.forward` for
more detailed explanation.
"""
assert isinstance(batch.obs, np.ndarray), "only support np.ndarray observation"
# TODO: shouldn't the model output a state as well if state is passed (i.e. RNNs are involved)?
act = self.model(batch.obs, state=state, info=batch.info)
return cast(ActBatchProtocol, Batch(act=act))
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def learn(self, batch: RolloutBatchProtocol, *args: Any, **kwargs: Any) -> TPSRLTrainingStats:
n_s, n_a = self.model.n_state, self.model.n_action
trans_count = np.zeros((n_s, n_a, n_s))
rew_sum = np.zeros((n_s, n_a))
rew_square_sum = np.zeros((n_s, n_a))
rew_count = np.zeros((n_s, n_a))
for minibatch in batch.split(size=1):
obs, act, obs_next = minibatch.obs, minibatch.act, minibatch.obs_next
obs_next = cast(np.ndarray, obs_next)
assert not isinstance(obs, BatchProtocol), "Observations cannot be Batches here"
trans_count[obs, act, obs_next] += 1
rew_sum[obs, act] += minibatch.rew
rew_square_sum[obs, act] += minibatch.rew**2
rew_count[obs, act] += 1
if self._add_done_loop and minibatch.done:
# special operation for terminal states: add a self-loop
trans_count[obs_next, :, obs_next] += 1
rew_count[obs_next, :] += 1
self.model.observe(trans_count, rew_sum, rew_square_sum, rew_count)
return PSRLTrainingStats( # type: ignore[return-value]
psrl_rew_mean=float(self.model.rew_mean.mean()),
psrl_rew_std=float(self.model.rew_std.mean()),
)
