Conic Blackwell Algorithm: Parameter-Free Convex-Concave Saddle-Point Solving

• URL: http://arxiv.org/abs/2105.13203v1
• Date: Thu, 27 May 2021 14:50:31 GMT
• Title: Conic Blackwell Algorithm: Parameter-Free Convex-Concave Saddle-Point Solving
• Authors: Julien Grand-Cl\'ement, Christian Kroer
• Abstract summary: We develop a new simple regret minimizer, the Conic Blackwell Algorithm$+$ (CBA$+$) We show how to implement CBA$+$ for the simplex, $ell_p$ norm balls, and ellipsoidal confidence regions in the simplex. We present numerical experiments for solving matrix games and distributionally robust optimization problems.
• Score: 21.496093093434357
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop new parameter and scale-free algorithms for solving convex-concave saddle-point problems. Our results are based on a new simple regret minimizer, the Conic Blackwell Algorithm$^+$ (CBA$^+$), which attains $O(1/\sqrt{T})$ average regret. Intuitively, our approach generalizes to other decision sets of interest ideas from the Counterfactual Regret minimization (CFR$^+$) algorithm, which has very strong practical performance for solving sequential games on simplexes. We show how to implement CBA$^+$ for the simplex, $\ell_{p}$ norm balls, and ellipsoidal confidence regions in the simplex, and we present numerical experiments for solving matrix games and distributionally robust optimization problems. Our empirical results show that CBA$^+$ is a simple algorithm that outperforms state-of-the-art methods on synthetic data and real data instances, without the need for any choice of step sizes or other algorithmic parameters.

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