2024/02/15 by Brian Hu Zhang, Ioannis Anagnostides, Zhang, Brian Hu +5 · 3 citations
Computer Science · #Generative Adversarial Networks and Image Synthesis #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2402.09670
Recent breakthrough results by Dagan, Daskalakis, Fishelson and Golowich [2023] and Peng and Rubinstein [2023] established an efficient algorithm attaining at most ε swap regret over extensive-form strategy spaces of dimension N in N O(1/ε) rounds. On the other extreme, Farina and Pipis [2023] developed an efficient algorithm for minimizing the weaker notion of linear-swap regret in poly(N)/ε2 rounds. In this paper, we develop efficient parameterized algorithms for regimes between these two extremes. We introduce the set of k-mediator deviations, which generalize the untimed communication deviations recently introduced by Zhang, Farina and Sandholm [2024] to the case of having multiple mediators, and we develop algorithms for minimizing the regret with respect to this set of deviations in NO(k)/ε2 rounds. Moreover, by relating k-mediator deviations to low-degree polynomials, we show that regret minimization against degree-k polynomial swap deviations is achievable in NO(kd)3/ε2 rounds, where d is the depth of the game, assuming a constant branching factor. For a fixed degree k, this is polynomial for Bayesian games and quasipolynomial more broadly when d = polylog N -- the usual balancedness assumption on the game tree.