{"ID":2871616,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.10989","arxiv_id":"2509.10989","title":"Actively Learning to Coordinate in Convex Games via Approximate Correlated Equilibrium","abstract":"Correlated equilibrium generalizes Nash equilibrium by allowing a central coordinator to guide players' actions through shared recommendations, similar to how routing apps guide drivers. We investigate how a coordinator can learn a correlated equilibrium in convex games where each player minimizes a convex cost function that depends on other players' actions, subject to convex constraints without knowledge of the players' cost functions. We propose a learning framework that learns an approximate correlated equilibrium by actively querying players' regrets, \\emph{i.e.}, the cost saved by deviating from the coordinator's recommendations. We first show that a correlated equilibrium in convex games corresponds to a joint action distribution over an infinite joint action space that minimizes all players' regrets. To make the learning problem tractable, we introduce a heuristic that selects finitely many representative joint actions by maximizing their pairwise differences. We then apply Bayesian optimization to learn a probability distribution over the selected joint actions by querying all players' regrets. The learned distribution approximates a correlated equilibrium by minimizing players' regrets. We demonstrate the proposed approach via numerical experiments on multi-user traffic assignment games in a shared transportation network.","short_abstract":"Correlated equilibrium generalizes Nash equilibrium by allowing a central coordinator to guide players' actions through shared recommendations, similar to how routing apps guide drivers. We investigate how a coordinator can learn a correlated equilibrium in convex games where each player minimizes a convex cost functio...","url_abs":"https://arxiv.org/abs/2509.10989","url_pdf":"https://arxiv.org/pdf/2509.10989v1","authors":"[\"Zhenlong Fang\",\"Aryan Deshwal\",\"Yue Yu\"]","published":"2025-09-13T21:45:28Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}