Online Learning and Solving Infinite Games with an ERM Oracle

Angelos Assos, Idan Attias, Yuval Dagan, Constantinos Daskalakis, Maxwell Fishelson

Research output: Contribution to journalConference articlepeer-review

Abstract

While ERM suffices to attain near-optimal generalization error in the stochastic learning setting, this is not known to be the case in the online learning setting, where algorithms for general concept classes rely on computationally inefficient oracles such as the Standard Optimal Algorithm (SOA). In this work, we propose an algorithm for online binary classification setting that relies solely on ERM oracle calls, and show that it has finite regret in the realizable setting and sublinearly growing regret in the agnostic setting. We bound the regret in terms of the Littlestone and threshold dimensions of the underlying concept class. We obtain similar results for nonparametric games, where the ERM oracle can be interpreted as a best response oracle, finding the best response of a player to a given history of play of the other players. In this setting, we provide learning algorithms that only rely on best response oracles and converge to approximate-minimax equilibria in two-player zero-sum games and approximate coarse correlated equilibria in multi-player general-sum games, as long as the game has a bounded fat-threshold dimension. Our algorithms apply to both binary-valued and real-valued games and can be viewed as providing justification for the wide use of double oracle and multiple oracle algorithms in the practice of solving large games.

Original languageEnglish
Pages (from-to)274-324
Number of pages51
JournalProceedings of Machine Learning Research
Volume195
StatePublished - 1 Jan 2023
Event36th Annual Conference on Learning Theory, COLT 2023 - Bangalore, India
Duration: 12 Jul 202315 Jul 2023

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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