Barriers to Welfare Maximization with No-Regret Learning

• URL: http://arxiv.org/abs/2411.01720v1
• Date: Mon, 04 Nov 2024 00:34:56 GMT
• Title: Barriers to Welfare Maximization with No-Regret Learning
• Authors: Ioannis Anagnostides, Alkis Kalavasis, Tuomas Sandholm,
• Abstract summary: We prove lower bounds for computing a near-optimal $T$-sparse CCE. In particular, we show that the inapproximability of maximum clique precludes attaining any non-trivial sparsity in time.
• Score: 68.66209476382213
• License:
• Abstract: A celebrated result in the interface of online learning and game theory guarantees that the repeated interaction of no-regret players leads to a coarse correlated equilibrium (CCE) -- a natural game-theoretic solution concept. Despite the rich history of this foundational problem and the tremendous interest it has received in recent years, a basic question still remains open: how many iterations are needed for no-regret players to approximate an equilibrium? In this paper, we establish the first computational lower bounds for that problem in two-player (general-sum) games under the constraint that the CCE reached approximates the optimal social welfare (or some other natural objective). From a technical standpoint, our approach revolves around proving lower bounds for computing a near-optimal $T$-sparse CCE -- a mixture of $T$ product distributions, thereby circumscribing the iteration complexity of no-regret learning even in the centralized model of computation. Our proof proceeds by extending a classical reduction of Gilboa and Zemel [1989] for optimal Nash to sparse (approximate) CCE. In particular, we show that the inapproximability of maximum clique precludes attaining any non-trivial sparsity in polynomial time. Moreover, we strengthen our hardness results to apply in the low-precision regime as well via the planted clique conjecture.

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