Sarsa

Sarsa 决策

• 学习完成后，根据当前状态在Q值表中的最大Q值来选取动作

Sarsa更新

• 更新Q值表：通过计算现实Q值和估计Q值的差距来更新
• 现实Q值：估算的动作也是接下来要做的动作（on-policy）
• 估计Q值：原Q值表中对应的Q值

Sarsa整体算法

• 不同之处：Sarsa是说到做到型，所以称为on-policy，在线学习，学着自己在做的事情。而Q-learning 是说到但并不一定做到，所以称为Off-policy，离线学习。

代码

"""
This part of code is the Q learning brain, which is a brain of the agent.
All decisions are made in here.

View more on my tutorial page: https://morvanzhou.github.io/tutorials/
"""

import numpy as np
import pandas as pd


class RL(object):
    def __init__(self, action_space, learning_rate=0.01, reward_decay=0.9, e_greedy=0.9):
        self.actions = action_space  # a list
        self.lr = learning_rate
        self.gamma = reward_decay
        self.epsilon = e_greedy

        self.q_table = pd.DataFrame(columns=self.actions, dtype=np.float64)

    def check_state_exist(self, state):
        if state not in self.q_table.index:
            # append new state to q table
            self.q_table = self.q_table.append(
                pd.Series(
                    [0]*len(self.actions),
                    index=self.q_table.columns,
                    name=state,
                )
            )

    def choose_action(self, observation):
        self.check_state_exist(observation)
        # action selection
        if np.random.rand() < self.epsilon:
            # choose best action
            state_action = self.q_table.loc[observation, :]
            # some actions may have the same value, randomly choose on in these actions
            action = np.random.choice(state_action[state_action == np.max(state_action)].index)
        else:
            # choose random action
            action = np.random.choice(self.actions)
        return action

    def learn(self, *args):
        pass


# off-policy
class QLearningTable(RL):
    def __init__(self, actions, learning_rate=0.01, reward_decay=0.9, e_greedy=0.9):
        super(QLearningTable, self).__init__(actions, learning_rate, reward_decay, e_greedy)

    def learn(self, s, a, r, s_):
        self.check_state_exist(s_)
        q_predict = self.q_table.loc[s, a]
        if s_ != 'terminal':
            q_target = r + self.gamma * self.q_table.loc[s_, :].max()  # next state is not terminal
        else:
            q_target = r  # next state is terminal
        self.q_table.loc[s, a] += self.lr * (q_target - q_predict)  # update


# on-policy
class SarsaTable(RL):

    def __init__(self, actions, learning_rate=0.01, reward_decay=0.9, e_greedy=0.9):
        super(SarsaTable, self).__init__(actions, learning_rate, reward_decay, e_greedy)

    def learn(self, s, a, r, s_, a_):
        self.check_state_exist(s_)
        q_predict = self.q_table.loc[s, a]
        if s_ != 'terminal':
            q_target = r + self.gamma * self.q_table.loc[s_, a_]  # next state is not terminal
        else:
            q_target = r  # next state is terminal
        self.q_table.loc[s, a] += self.lr * (q_target - q_predict)  # update

Sarsa(λ)

单步更新 and 回合更新

λ取值

• 当λ=0, 就变成了Sarsa的单步更新, 当λ=1, 就变成了回合更新, 对所有步更新的力度都是一样。 当λ=(0,1)之间, 取值越大, 离宝藏越近的步更新力度越大。

Sarsa(λ)整体算法

代码

"""
This part of code is the Q learning brain, which is a brain of the agent.
All decisions are made in here.

View more on my tutorial page: https://morvanzhou.github.io/tutorials/
"""

import numpy as np
import pandas as pd


class RL(object):
    def __init__(self, action_space, learning_rate=0.01, reward_decay=0.9, e_greedy=0.9):
        self.actions = action_space  # a list
        self.lr = learning_rate
        self.gamma = reward_decay
        self.epsilon = e_greedy

        self.q_table = pd.DataFrame(columns=self.actions, dtype=np.float64)

    def check_state_exist(self, state):
        if state not in self.q_table.index:
            # append new state to q table
            self.q_table = self.q_table.append(
                pd.Series(
                    [0]*len(self.actions),
                    index=self.q_table.columns,
                    name=state,
                )
            )

    def choose_action(self, observation):
        self.check_state_exist(observation)
        # action selection
        if np.random.rand() < self.epsilon:
            # choose best action
            state_action = self.q_table.loc[observation, :]
            # some actions may have the same value, randomly choose on in these actions
            action = np.random.choice(state_action[state_action == np.max(state_action)].index)
        else:
            # choose random action
            action = np.random.choice(self.actions)
        return action

    def learn(self, *args):
        pass


# backward eligibility traces
class SarsaLambdaTable(RL):
    def __init__(self, actions, learning_rate=0.01, reward_decay=0.9, e_greedy=0.9, trace_decay=0.9):
        super(SarsaLambdaTable, self).__init__(actions, learning_rate, reward_decay, e_greedy)

        # backward view, eligibility trace.
        self.lambda_ = trace_decay
        self.eligibility_trace = self.q_table.copy()

    def check_state_exist(self, state):
        if state not in self.q_table.index:
            # append new state to q table
            to_be_append = pd.Series(
                    [0] * len(self.actions),
                    index=self.q_table.columns,
                    name=state,
                )
            self.q_table = self.q_table.append(to_be_append)

            # also update eligibility trace
            self.eligibility_trace = self.eligibility_trace.append(to_be_append)

    def learn(self, s, a, r, s_, a_):
        self.check_state_exist(s_)
        q_predict = self.q_table.loc[s, a]
        if s_ != 'terminal':
            q_target = r + self.gamma * self.q_table.loc[s_, a_]  # next state is not terminal
        else:
            q_target = r  # next state is terminal
        error = q_target - q_predict

        # increase trace amount for visited state-action pair

        # Method 1:
        # self.eligibility_trace.loc[s, a] += 1

        # Method 2:
        self.eligibility_trace.loc[s, :] *= 0
        self.eligibility_trace.loc[s, a] = 1

        # Q update
        self.q_table += self.lr * error * self.eligibility_trace

        # decay eligibility trace after update
        self.eligibility_trace *= self.gamma*self.lambda_