Provably Optimal Learning Algorithms for Assistance Games

2026-07-08

AI Summary

This work studies efficient coordination under asymmetric information in repeated online assisted games with a shared reward, where the informed player (human) observes a hidden state while the uninformed assistant only sees the human’s actions. The paper introduces, for the first time, a provably efficient decentralized learning algorithm that leverages the novel notion of “assistance regret.” It establishes that achieving a $(1 - 1/e)$ approximation factor is computationally infeasible in this setting. By combining any no-regret learner with a shared random seed, the proposed method attains an optimal $\widetilde{O}(T^{1/2})$ regret bound in a pseudo-decentralized framework and achieves a $(1 - 1/e)$-approximate assistance regret bound of $\widetilde{O}(T^{3/4})$.

Abstract

This paper studies an online variant of the assistance games framework, where an informed agent and an uninformed agent repeatedly interact over $T$ timesteps to optimize a common reward function. While the informed agent (the human) observes a latent state of the world, the uninformed agent (the assistant) observes only the human's actions. We provide the first provably efficient learning algorithms for repeated assistance games. We introduce the notion of assistance regret: the gap between the cumulative utility of interactions and that of the optimal joint policies in hindsight, which map latent states to action pairs. We present decentralized algorithms for both the human and the assistant that achieve a $(1-1/e)$-approximate assistance regret rate of $\widetilde{O}(T^{3/4})$, with runtime polynomial in the size of the action and state spaces. These algorithms are general; in particular, they accommodate any no-regret algorithm for the assistant. We prove that achieving a regret approximation factor better than $(1-1/e)$ is computationally intractable. Furthermore, we demonstrate how these generic no-regret algorithms can be tailored to a pseudo-decentralized setting -- using a shared random string -- to achieve a rate of $\widetilde{O}(T^{1/2})$, optimal up to logarithmic factors.

Problem

• assistance games
• online learning
• information asymmetry
• regret minimization
• multi-agent coordination

Innovation

• assistance games
• assistance regret
• decentralized learning
• no-regret algorithms
• online learning