强化学习Q-learning求最优策略

理论基础：

on policy：behavior policy=target policy

off policy：behavior policy!=target policy

注意：

behavior policy的初始化最好具有较强的随机性，就能尽可能遍历到所有的(s, a)pair。

强化学习的数据基础这种书中有不同的behavior policy导致的不同的探索路径的图：

代码可运行：

import numpy as np from env import GridWorldEnv from utils import drow_policy class Q_Learning(object): def __init__(self, env: GridWorldEnv, gamma=0.9, alpha=0.001, epsilon=0.1, samples=1, start_state=(0, 0),mode="on policy"): ''' :param env: 定义了网格的基础配置 :param gamma: discount rate :param alpha: learning rate :param samples: 从起点到终点采样的路径数 :param start_state: 起点 :param mode: 模式 ''' self.env = env self.action_space_size = self.env.num_actions # 上下左右原地 self.state_space_size = self.env.num_states self.reward_list = self.env.reward_list self.gamma = gamma self.samples = samples self.alpha = alpha self.epsilon = epsilon self.mode=mode self.start_state = self.env.state_id(start_state[0], start_state[1]) self.behavior_policy = np.ones( (self.state_space_size, self.action_space_size)) / self.action_space_size # 探索性很强 self.target_policy = np.zeros((self.state_space_size, self.action_space_size)) self.qvalues = np.zeros((self.state_space_size, self.action_space_size)) def update_qvalues(self,s_t,a_t,s_next,r_next): max_q_next = np.max(self.qvalues[s_next]) td_target = r_next + self.gamma * max_q_next td_error = td_target - self.qvalues[s_t][a_t] # 负号提出去 self.qvalues[s_t][a_t] += self.alpha * td_error def solve(self): if self.mode=="off policy": for _ in range(self.samples): s = self.start_state a = np.random.choice(self.action_space_size, p=self.behavior_policy[s]) episode = self.env.generate_episodes(self.behavior_policy, s, a) for i in range(len(episode)): s_t, a_t, r_next_t, s_next_t= episode[i] self.update_qvalues(s_t,a_t,s_next_t,r_next_t) # greedy best_a = np.argmax(self.qvalues[s_t]) self.target_policy[s_t] = np.eye(self.action_space_size)[best_a] elif self.mode=="on policy": # target_policy=behavior_policy for _ in range(self.samples): s = self.start_state while s not in self.env.terminal: a = np.random.choice(self.action_space_size, p=self.behavior_policy[s]) # generate at following πt(st) next_s, next_r, _ = self.env.step(s, a) # generate rt+1, st+1 by interacting with the environment # updata q-value for (s_t,a_t) # qt+1(st, at) = qt(st, at) − αt(st, at) [ qt(st, at) − (rt+1 + γ max(qt(st+1, a)))] self.update_qvalues(s,a,next_s,next_r) # update policy for s_t: epsilon greedy 因为要用policy生成数据，因此需要策略具有一定的探索性，因此使用epsilon greedy best_a = np.argmax(self.qvalues[s]) self.behavior_policy[s] = self.epsilon / self.action_space_size self.behavior_policy[s, best_a] += 1 - self.epsilon self.target_policy=self.behavior_policy s = next_s else: raise Exception("Invalid mode") if __name__ == '__main__': env = GridWorldEnv( size=5, forbidden=[(1, 2), (3, 3)], terminal=[(4, 4)], r_boundary=-1, r_other=-0.04, r_terminal=1, r_forbidden=-1, r_stay=-0.1 ) # 注意samples要大一点，否则每个state被访问到的概率很小 vi = Q_Learning(env=env, gamma=0.8, alpha=0.01, samples=1000, start_state=(0, 0),mode="off policy") vi.solve() print("\n state value: ") print(vi.qvalues) drow_policy(vi.target_policy, env)