Sarsa-lambda是Sarsa演算法的一種提速的方法。

如果說 Sarsa 和 Qlearning 都是每次獲取到 reward, 只更新獲取到 reward 的前一步. 那 Sarsa-lambda 就是更新獲取到 reward 的前 lambda 步. lambda 是在 [0, 1] 之間取值,

如果 lambda = 0, Sarsa-lambda 就是 Sarsa, 只更新獲取到 reward 前經歷的最後一步.

如果 lambda = 1, Sarsa-lambda 更新的是 獲取到 reward 前所有經歷的步.（來自於https://morvanzhou.github.io/tutorials/machine-learning/reinforcement-learning/3-3-tabular-sarsa-lambda/

lambda的含義：

lambda 就是一個衰變值, 他可以讓你知道離獎勵越遠的步可能並不是讓你最快拿到獎勵的步, 所以我們想象我們站在寶藏的位置, 回頭看看我們走過的尋寶之路, 離寶藏越近的腳印越看得清, 遠處的腳印太渺小, 我們都很難看清, 那我們就索性記下離寶藏越近的腳印越重要, 越需要被好好的更新. 和之前我們提到過的 獎勵衰減值 gamma 一樣, lambda 是腳步衰減值, 都是一個在 0 和 1 之間的數.

程式碼實現走迷宮的小例子（來自於莫凡大神https://github.com/MorvanZhou/Reinforcement-learning-with-tensorflow/tree/master/contents/4_Sarsa_lambda_maze

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_