Abstract
A seminal study showed repeated games with vector payoffs, which has had wide-ranging applications to decision making under uncertainty. Although this study characterized the achievable guarantees in such games under the long-run average payoff criterion, the characterization and computation of these guarantees under the discounted payoff criterion have remained a significant gap in the literature. In “An Approximate Dynamic Programming Approach to Repeated Games with Vector Losses,” V. Kamble, P. Loiseau, and J. Walrand develop a set-valued dynamic programming approach along with an approximation framework to fully address this problem. This theory results in new algorithms that beat the state of the art for applications such as exact regret minimization in the well-known problem of prediction under expert advice.
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