Learning in games with continuous action sets and unknown payoff functions

• Published in: Mathematical programming Vol. 173; no. 1-2; pp. 465 - 507
• Main Authors: Mertikopoulos, Panayotis, Zhou, Zhengyuan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2019; Springer Nature B.V
• Subjects: Algorithms; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Convergence; Distance learning; Equilibrium; Error analysis; Feedback; Full Length Paper; Game theory; Games; Learning; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Optimization; Theoretical; Variational stability; Continuous games; Dual averaging; Primary 91A26; Fenchel coupling; Secondary 90C33; Nash equilibrium; 90C15; 68Q32

This paper examines the convergence of no-regret learning in games with continuous action sets. For concreteness, we focus on learning via “dual averaging”, a widely used class of no-regret learning schemes where players take small steps along their individual payoff gradients and then “mirror” the...