FrozenLake with Expected SARSA

In this notebook we solve a non-slippery version of the FrozenLake-v0 environment using value-based control with Expected SARSA bootstrap targets.

We’ll use a linear function approximator for our state-action value function \(q_\theta(s,a)\). Since the observation space is discrete, this is equivalent to the table-lookup case.

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expected_sarsa.py

import coax
import gymnasium
import jax
import jax.numpy as jnp
import haiku as hk
import optax


# the MDP
env = gymnasium.make('FrozenLakeNonSlippery-v0')
env = coax.wrappers.TrainMonitor(env)


def func(S, A, is_training):
    value = hk.Sequential((hk.Flatten(), hk.Linear(1, w_init=jnp.zeros), jnp.ravel))
    X = jax.vmap(jnp.kron)(S, A)  # S and A are one-hot encoded
    return value(X)


# function approximator
q = coax.Q(func, env)
pi = coax.BoltzmannPolicy(q, temperature=0.1)


# experience tracer
tracer = coax.reward_tracing.NStep(n=1, gamma=0.9)


# updater
esarsa = coax.td_learning.ExpectedSarsa(q, pi, optimizer=optax.adam(0.02))


# train
for ep in range(500):
    s, info = env.reset()

    for t in range(env.spec.max_episode_steps):
        a = pi(s)
        s_next, r, done, truncated, info = env.step(a)

        # small incentive to keep moving
        if jnp.array_equal(s_next, s):
            r = -0.01

        # update
        tracer.add(s, a, r, done or truncated)
        while tracer:
            transition_batch = tracer.pop()
            esarsa.update(transition_batch)

        if done or truncated:
            break

        s = s_next

    # early stopping
    if env.avg_G > env.spec.reward_threshold:
        break


# run env one more time to render
s, info = env.reset()
env.render()

for t in range(env.spec.max_episode_steps):

    # print individual state-action values
    for i, q_ in enumerate(q(s)):
        print("  q(s,{:s}) = {:.3f}".format('LDRU'[i], q_))

    a = pi.mode(s)
    s, r, done, truncated, info = env.step(a)

    env.render()

    if done or truncated:
        break


if env.avg_G < env.spec.reward_threshold:
    name = globals().get('__file__', 'this script')
    raise RuntimeError(f"{name} failed to reach env.spec.reward_threshold")