To develop a Python program to find the optimal policy for the given RL environment using SARSA-Learning and compare the state values with the Monte Carlo method.
The bandit slippery walk problem is a reinforcement learning problem in which an agent must learn to navigate a 7-state environment in order to reach a goal state. The environment is slippery, so the agent has a chance of moving in the opposite direction of the action it takes.
The environment has 7 states:
- Two Terminal States: G: The goal state & H: A hole state.
- Five Transition states / Non-terminal States including S: The starting state.
The agent can take two actions:
- R: Move right.
- L: Move left.
The transition probabilities for each action are as follows:
- 50% chance that the agent moves in the intended direction.
- 33.33% chance that the agent stays in its current state.
- 16.66% chance that the agent moves in the opposite direction. For example, if the agent is in state S and takes the "R" action, then there is a 50% chance that it will move to state 4, a 33.33% chance that it will stay in state S, and a 16.66% chance that it will move to state 2.
The agent receives a reward of +1 for reaching the goal state (G). The agent receives a reward of 0 for all other states.
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Initialize the Q-values arbitrarily for all state-action pairs.
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Repeat for each episode:
i. Initialize the starting state.
ii. Repeat for each step of episode:
a. Choose action from state using policy derived from Q (e.g., epsilon-greedy). b. Take action, observe reward and next state. c. Choose action from next state using policy derived from Q (e.g., epsilon-greedy). d. Update Q(s, a) := Q(s, a) + alpha * [R + gamma * Q(s', a') - Q(s, a)] e. Update the state and action.
iii. Until state is terminal.
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Until performance converges.
def sarsa(env,
gamma=1.0,
init_alpha=0.5,
min_alpha=0.01,
alpha_decay_ratio=0.5,
init_epsilon=1.0,
min_epsilon=0.1,
epsilon_decay_ratio=0.9,
n_episodes=3000):
nS, nA = env.observation_space.n, env.action_space.n
pi_track = []
Q = np.zeros((nS, nA), dtype=np.float64)
Q_track = np.zeros((n_episodes, nS, nA), dtype=np.float64)
# Write your code here
select_action = lambda state, Q, epsilon:np.argmax(Q[state]) if np.random.random() > epsilon else np.random.randint(len(Q[state]))
alphas = decay_schedule(init_alpha, min_alpha,
alpha_decay_ratio, n_episodes)
epsilons = decay_schedule(init_epsilon, min_epsilon,
epsilon_decay_ratio, n_episodes)
for e in tqdm(range(n_episodes), leave=False):
state, done = env.reset(), False
action = select_action(state, Q, epsilons[e])
while not done:
next_state, reward, done, _= env.step(action)
next_action = select_action(next_state, Q, epsilons[e])
td_target = reward + gamma * Q[next_state][next_action] * (not done)
td_error = td_target - Q[state][action]
Q[state][action] = Q[state][action] + alphas[e] * td_error
state, action = next_state, next_action
Q_track[e] = Q
pi_track.append(np.argmax(Q, axis=1))
V = np.max(Q, axis=1)
pi = lambda s: {s:a for s, a in enumerate(np.argmax(Q, axis=1))}[s]
return Q, V, pi, Q_track, pi_track
Thus, the implementation of SARSA learning algorithm was implemented successfully.