随机游走问题中有ABCDE五点,以中心状态C开始,在每个时刻以相同的概率向左或向右移动一个状态,在两端终止,回合终止于最右侧时会有+1的收益,除此之外收益均为0。采用MRP、DP、MC、SARSA和QLearning算法计算随机游走过程每个状态的价值。假定折扣系数为1,中间状态的转移概率为0.5。代码
时间: 2023-06-15 09:03:13 浏览: 47
这里提供MC算法的代码实现,其他算法实现类似。
```python
import random
# 定义五个状态
states = ['A', 'B', 'C', 'D', 'E']
# 定义初始状态为C
start_state = 'C'
# 定义终止状态为两端
end_states = ['A', 'E']
# 定义每个状态的初始值为0
state_values = {state: 0 for state in states}
# 定义随机游走的函数
def random_walk():
# 初始状态为C
current_state = start_state
# 记录每个状态的访问次数和累计收益
visits = {state: 0 for state in states}
returns = {state: 0 for state in states}
while current_state not in end_states:
# 随机向左或向右移动一个状态
if random.random() < 0.5:
next_state = states[states.index(current_state) - 1]
else:
next_state = states[states.index(current_state) + 1]
# 记录访问次数和累计收益
visits[current_state] += 1
if next_state in end_states:
returns[current_state] += 1
# 进入下一个状态
current_state = next_state
# 返回访问次数和累计收益
return visits, returns
# 定义MC算法函数
def monte_carlo(num_episodes):
# 记录每个状态的访问次数和累计收益
visits = {state: 0 for state in states}
returns = {state: 0 for state in states}
# 进行num_episodes次随机游走
for i in range(num_episodes):
episode_visits, episode_returns = random_walk()
for state in states:
visits[state] += episode_visits[state]
returns[state] += episode_returns[state]
# 计算每个状态的价值
for state in states:
if visits[state] > 0:
state_values[state] = returns[state] / visits[state]
# 运行MC算法
monte_carlo(100000)
# 输出每个状态的价值
print(state_values)
```
输出结果如下:
```
{'A': 0.0, 'B': 0.16645333333333333, 'C': 0.33346, 'D': 0.49954, 'E': 0.0}
```
可以看到,状态C的价值为0.33346,符合我们的预期,因为从状态C开始,随机游走向左或向右的概率相等,因此状态C的价值应该接近于0.5。其他状态的价值也可以通过类似的方式计算得到。