Multi-Agent Learning in Contextual Games under Unknown Constraints
Anna M. Maddux, Maryam Kamgarpour
Abstract
We consider the problem of learning to play a repeated contextual game with unknown reward and unknown constraints functions. Such games arise in applications where each agent’s action needs to belong to a feasible set, but the feasible set is a priori unknown. For example, in constrained multi-agent reinforcement learning, the constraints on the agents’ policies are a function of the unknown dynamics and hence, are themselves unknown. Under kernel-based regularity assumptions on the unknown functions, we develop a no-regret, no-violation approach that exploits similarities among different reward and constraint outcomes. The no-violation property ensures that the time-averaged sum of constraint violations converges to zero as the game is repeated. We show that our algorithm referred to as c.z.AdaNormalGP, obtains kernel-dependent regret bounds, and the cumulative constraint violations have sublinear kernel-dependent upper bounds. In addition, we introduce the notion of constrained contextual coarse correlated equilibria (c.z.CCE) and show that $\epsilon$-c.z.CCEs can be approached whenever players follow a no-regret no-violation strategy. Finally, we experimentally demonstrate the effectiveness of c.z.AdaNormalGP on an instance of multi-agent reinforcement learning.
BibTeX
@InProceedings{pmlr-v238-maddux24a,
title = {Multi-Agent Learning in Contextual Games under Unknown Constraints},
author = {Maddux, Anna M. and Kamgarpour, Maryam},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {3142--3150},
year = {2024},
editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
volume = {238},
series = {Proceedings of Machine Learning Research},
month = {02--04 May},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v238/maddux24a/maddux24a.pdf},
url = {https://proceedings.mlr.press/v238/maddux24a.html},
abstract = {We consider the problem of learning to play a repeated contextual game with unknown reward and unknown constraints functions. Such games arise in applications where each agent’s action needs to belong to a feasible set, but the feasible set is a priori unknown. For example, in constrained multi-agent reinforcement learning, the constraints on the agents’ policies are a function of the unknown dynamics and hence, are themselves unknown. Under kernel-based regularity assumptions on the unknown functions, we develop a no-regret, no-violation approach that exploits similarities among different reward and constraint outcomes. The no-violation property ensures that the time-averaged sum of constraint violations converges to zero as the game is repeated. We show that our algorithm referred to as c.z.AdaNormalGP, obtains kernel-dependent regret bounds, and the cumulative constraint violations have sublinear kernel-dependent upper bounds. In addition, we introduce the notion of constrained contextual coarse correlated equilibria (c.z.CCE) and show that $\epsilon$-c.z.CCEs can be approached whenever players follow a no-regret no-violation strategy. Finally, we experimentally demonstrate the effectiveness of c.z.AdaNormalGP on an instance of multi-agent reinforcement learning.}
}