Solving Optimization Problems with Blackwell Approachability

In this paper, we propose a new algorithm for solving convex-concave saddle-point problems using regret minimization in the repeated game framework. To do so, introduce Conic Blackwell Algorithm + ([Formula: see text]), parameter- and scale-free minimizer general convex compact sets. [Formula: text] is based on approachability attains regret. We show how to efficiently instantiate many decision sets of interest, including simplex, norm balls, ellipsoidal confidence regions simplex. Based text], parameter-free achieving ergodic convergence rate. our simulations, demonstrate wide applicability several standard from optimization operations research literature, matrix games, extensive-form distributionally robust logistic regression, Markov processes. each setting, achieves state-of-the-art numerical performance outperforms classical methods, without need any choice step sizes or other algorithmic parameters. Funding: J. Grand-Clément supported by Agence Nationale de la Recherche [Grant 11-LABX-0047] Hi! Paris. C. Kroer Office Naval Research N00014-22-1-2530] National Science Foundation IIS-2147361].