Sarsa algorithm, why Q-values tend to zero?

Question

I'm trying to implement Sarsa algorithm for solving a Frozen Lake environment from OpenAI gym. I've started soon to work with this but I think I understand it.

I also understand how Sarsa algorithm works, there're many sites where to find a pseudocode, and I get it. I've implemented this algorithm in my problem following all the steps, but when I check the final Q function after all the episodes I notice that all values tend to zero and I don't know why.

Here is my code, I hope someone can tell me why that happens.

import gym
import random
import numpy as np

env = gym.make('FrozenLake-v0')

#Initialize the Q matrix 16(rows)x4(columns)
Q = np.zeros([env.observation_space.n, env.action_space.n])

for i in range(env.observation_space.n):
    if (i != 5) and (i != 7) and (i != 11) and (i != 12) and (i != 15):
        for j in range(env.action_space.n):
            Q[i,j] = np.random.rand()

#Epsilon-Greedy policy, given a state the agent chooses the action that it believes has the best long-term effect with probability 1-eps, otherwise, it chooses an action uniformly at random. Epsilon may change its value.

bestreward = 0
epsilon = 0.1
discount = 0.99
learning_rate = 0.1
num_episodes = 50000
a = [0,0,0,0,0,0,0,0,0,0]

for i_episode in range(num_episodes):

    # Observe current state s
    observation = env.reset()
    currentState = observation

    # Select action a using a policy based on Q
    if np.random.rand() <= epsilon: #pick randomly
        currentAction = random.randint(0,env.action_space.n-1)
    else: #pick greedily            
        currentAction = np.argmax(Q[currentState, :])

    totalreward = 0
    while True:
        env.render()

        # Carry out an action a 
        observation, reward, done, info = env.step(currentAction)
        if done is True:
            break;

        # Observe reward r and state s'
        totalreward += reward
        nextState = observation

        # Select action a' using a policy based on Q
        if np.random.rand() <= epsilon: #pick randomly
            nextAction = random.randint(0,env.action_space.n-1)
        else: #pick greedily            
            nextAction = np.argmax(Q[nextState, :])

        # update Q with Q-learning 
        Q[currentState, currentAction] += learning_rate * (reward + discount * Q[nextState, nextAction] - Q[currentState, currentAction])

        currentState = nextState
        currentAction = nextAction

        print "Episode: %d reward %d best %d epsilon %f" % (i_episode, totalreward, bestreward, epsilon)
        if totalreward > bestreward:
            bestreward = totalreward
        if i_episode > num_episodes/2:
            epsilon = epsilon * 0.9999
        if i_episode >= num_episodes-10:
            a.insert(0, totalreward)
            a.pop()
        print a

        for i in range(env.observation_space.n):
            print "-----"
            for j in range(env.action_space.n):
                print Q[i,j]

Answer 1

When a episode ends you are breaking the while loop before updating the Q function. Therefore, when the reward received by the agent is different from zero (the agent has reached the goal state), the Q function is never updated in that reward.

You should check for the end of the episode in the last part of the while loop.