马尔科夫决策过程代码

马尔科夫决策过程（Markov Decision Process，MDP）一种用于描述序贯决策问题的数学模型。在代码实现上，可以使用Python的相关库来构和求解MDP问题，例如使用numpy和gym库。

下面是一个简单的马尔科夫决策过程代码示例：

import numpy as np

# 定义MDP的状态空间、动作空间、状态转移概率和奖励函数
states = ['S1', 'S2', 'S3']  # 状态空间
actions = ['A1', 'A2']  # 动作空间
transition_probs = {
    'S1': {
        'A1': {'S1': 0.2, 'S2': 0.8},
        'A2': {'S2': 1.0}
    },
    'S2': {
        'A1': {'S1': 0.6, 'S3': 0.4},
        'A2': {'S3': 1.0}
    },
    'S3': {
        'A1': {'S3': 1.0},
        'A2': {'S1': 0.7, 'S3': 0.3}
    }
}
rewards = {
    'S1': {'A1': {'S1': -10, 'S3': 5}, 'A2': {'S3': 0}},
    'S3': {'A1': {'S3': 0}, 'A2': {'S1': 20, 'S3': -5}}
}

# 定义MDP的价值函数和策略
values = {state: 0 for state in states}  # 价值函数
policy = {state: np.random.choice(actions) for state in states}  # 策略

# 迭代求解MDP的最优策略和最优价值函数
discount_factor = 0.9  # 折扣因子
num_iterations = 100  # 迭代次数

for _ in range(num_iterations):
    new_values = {}
    for state in states:
        action = policy[state]
        new_value = sum(transition_probs[state][action][next_state] * (rewards[state][action][next_state] + discount_factor * values[next_state]) for next_state in states)
        new_values[state] = new_value
    values = new_values

    new_policy = {}
    for state in states:
        action_values = {action: sum(transition_probs[state][action][next_state] * (rewards[state][action][next_state] + discount_factor * values[next_state]) for next_state in states) for action in actions}
        best_action = max(action_values, key=action_values.get)
        new_policy[state] = best_action
    policy = new_policy

# 输出最优策略和最优价值函数
print("Optimal Policy:")
for state, action in policy.items():
    print(f"State: {state}, Action: {action}")
print("Optimal Values:")
for state, value in values.items():
    print(f"State: {state}, Value: {value}")

这段代码实现了一个简单的马尔科夫决策过程，包括定义状态空间、动作空间、状态转移概率和奖励函数，以及迭代求解最优策略和最优价值函数。在代码中，使用了折扣因子来衡量未来奖励的重要性，并通过迭代更新价值函数和策略来逐步优化。