2023/11/04 by Victor Boone, Panayotis Mertikopoulos, Boone, Victor +1 · 2 citations
Decision Sciences · Social Sciences · #62L20 #91A26 #Advanced Bandit Algorithms Research #Computer Science and Game Theory (cs.GT) #Experimental Behavioral Economics Studies #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Primary 91A10 #secondary 68Q32
paper · pdf · doi:10.48550/arxiv.2311.02407
openalex publication_date 2023/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we examine the long-run behavior of regularized, no-regret learning in finite games. A well-known result in the field states that the empirical frequencies of no-regret play converge to the game's set of coarse correlated equilibria; however, our understanding of how the players' actual strategies evolve over time is much more limited - and, in many cases, non-existent. This issue is exacerbated further by a series of recent results showing that only strict Nash equilibria are stable and attracting under regularized learning, thus making the relation between learning and pointwise solution concepts particularly elusive. In lieu of this, we take a more general approach and instead seek to characterize the setwise rationality properties of the players' day-to-day play. To that end, we focus on one of the most stringent criteria of setwise strategic stability, namely that any unilateral deviation from the set in question incurs a cost to the deviator - a property known as closedness under better replies (club). In so doing, we obtain a far-reaching equivalence between strategic and dynamic stability: a product of pure strategies is closed under better replies if and only if its span is stable and attracting under regularized learning. In addition, we estimate the rate of convergence to such sets, and we show that methods based on entropic regularization (like the exponential weights algorithm) converge at a geometric rate, while projection-based methods converge within a finite number of iterations, even with bandit, payoff-based feedback.