Q-learning and SARSA updates · Ingénierie IA

Tabular Q-learning and SARSA learn a table of action values from one transition at a time. Both move Q[s, a] toward a target. Q-learning uses the best next action in the target. SARSA uses the next action that the agent really takes. An epsilon-greedy policy picks the actions while the table learns.

Task

Write three functions.

q_learning_update(Q, s, a, r, s_next, done, alpha=0.1, gamma=0.99) returns the table after one Q-learning update.
sarsa_update(Q, s, a, r, s_next, a_next, done, alpha=0.1, gamma=0.99) returns the table after one SARSA update.
epsilon_greedy(Q, s, epsilon, rng) returns the action for state s.

Both updates change only the entry Q[s, a]:

Q[s, a] \leftarrow Q[s, a] + \alpha \left(y - Q[s, a]\right)

The target y for Q-learning is r + \gamma \max_{a'} Q[s', a']. The target for SARSA is r + \gamma \, Q[s', a_{next}]. When done is True, the target is r only, with no term for the next state. The target uses the values of Q before the update.

epsilon_greedy uses the generator rng in this exact order:

Draw u = rng.random().
If u < epsilon, draw and return rng.integers(n_actions).
Else return the action with the largest Q[s]. On a tie, return the lowest index.

Input and output

Name	Type	Shape	Meaning
`Q`	float array	`(n_states, n_actions)`	the action values
`s`, `s_next`	int		the state and the next state
`a`, `a_next`	int		the action and the next action
`r`	float		the reward of the transition
`done`	bool		`True` when `s_next` is terminal
`alpha`	float		the step size, from 0 to 1
`gamma`	float		the discount, from 0 to 1
`epsilon`	float		the probability of a random action, from 0 to 1
`rng`	`np.random.Generator`		the random generator

q_learning_update and sarsa_update return a new float array of shape (n_states, n_actions).
epsilon_greedy returns a Python int.

Constraints

1 <= n_states <= 1000 and 1 <= n_actions <= 20.
s_next can be equal to s.
Do not change the input table. Return a new table.
Use numpy only.

Examples

python

Q = np.array([[0.0, 1.0], [2.0, -1.0], [0.5, 0.5]])
q_learning_update(Q, 0, 1, -1.0, 1, False, alpha=0.5, gamma=0.9)
sarsa_update(Q, 0, 1, -1.0, 1, 1, False, alpha=0.5, gamma=0.9)
q_learning_update(Q, 0, 1, -1.0, 1, True, alpha=0.5, gamma=0.9)

text

[[ 0.   0.9]
 [ 2.  -1. ]
 [ 0.5  0.5]]
[[ 0.   -0.45]
 [ 2.   -1.  ]
 [ 0.5   0.5 ]]
[[ 0.   0. ]
 [ 2.  -1. ]
 [ 0.5  0.5]]

python

rng = np.random.default_rng(7)
Q = np.array([[1.0, 3.0, 3.0, 0.0]])
[epsilon_greedy(Q, 0, 0.5, rng) for _ in range(12)]

text

[1, 1, 1, 0, 1, 1, 1, 1, 3, 1, 3, 1]