import numpy as np
from copy import deepcopy
[docs]def value_iteration(prob, reward, gamma, eps):
"""
Value iteration algorithm to solve a dynamic programming problem.
Args:
prob (np.ndarray): transition probability matrix;
reward (np.ndarray): reward matrix;
gamma (float): discount factor;
eps (float): accuracy threshold.
Returns:
The optimal value of each state.
"""
n_states = prob.shape[0]
n_actions = prob.shape[1]
value = np.zeros(n_states)
while True:
value_old = deepcopy(value)
for state in range(n_states):
vmax = -np.inf
for action in range(n_actions):
prob_state_action = prob[state, action, :]
reward_state_action = reward[state, action, :]
va = prob_state_action.T.dot(
reward_state_action + gamma * value_old)
vmax = max(va, vmax)
value[state] = vmax
if np.linalg.norm(value - value_old) <= eps:
break
return value
[docs]def policy_iteration(prob, reward, gamma):
"""
Policy iteration algorithm to solve a dynamic programming problem.
Args:
prob (np.ndarray): transition probability matrix;
reward (np.ndarray): reward matrix;
gamma (float): discount factor.
Returns:
The optimal value of each state and the optimal policy.
"""
n_states = prob.shape[0]
n_actions = prob.shape[1]
policy = np.zeros(n_states, dtype=int)
value = np.zeros(n_states)
changed = True
while changed:
p_pi = np.zeros((n_states, n_states))
r_pi = np.zeros(n_states)
i = np.eye(n_states)
for state in range(n_states):
action = policy[state]
p_pi_s = prob[state, action, :]
r_pi_s = reward[state, action, :]
p_pi[state, :] = p_pi_s.T
r_pi[state] = p_pi_s.T.dot(r_pi_s)
value = np.linalg.solve(i - gamma * p_pi, r_pi)
changed = False
for state in range(n_states):
vmax = value[state]
for action in range(n_actions):
if action != policy[state]:
p_sa = prob[state, action]
r_sa = reward[state, action]
va = p_sa.T.dot(r_sa + gamma * value)
if va > vmax and not np.isclose(va, vmax):
policy[state] = action
vmax = va
changed = True
return value, policy