Exploration in the Face of Strategic Responses: Provable Learning of Online Stackelberg Games

ICLR 2025 Conference Submission12968 Authors

Keywords: Stackelberg game, RL, exploration

TL;DR: We propose a provably sample efficient algorithm for Markov Stackelberg games in the online setting

Abstract:

We study online leader-follower games where the leader interacts with a myopic follower using a quantal response policy. The leader's objective is to design an algorithm without prior knowledge of her reward function or the state transition dynamics.
Crucially, the leader also lacks insight into the follower's reward function and realized rewards, posing a significant challenge.
To address this, the leader must learn the follower's quantal response mapping solely through strategic interactions --- announcing policies and observing responses.
We introduce a unified algorithm, Planning after Estimation, which updates the leader's policies in a two-step approach.
In particular, we first jointly estimate the leader's value function and the follower's response mapping by maximizing a sum of the Bellman error of the value function, the likelihood of the quantal response model, and a regularization term that encourages exploration. The leader's policy is then updated through a greedy planning step based on these estimates. Our algorithm achieves a $\sqrt{T}$-regret in the context of general function approximation.
Moroever, this algorithm avoids the intractable optimistic planning and thus enhances implementation simplicity.

Primary Area: reinforcement learning

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Submission Number: 12968