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A recent paper by Piliouras et al. [2021, 2022] introduces an uncoupledlearning algorithm for normal-form games -- called Clairvoyant MWU (CMWU). Inthis note we show that CMWU is equivalent to the conceptual prox methoddescribed by Nemirovski [2004]. This connection immediately shows that it ispossible to extend the CMWU algorithm to any convex game, a question left openby Piliouras et al. We call the resulting algorithm -- again equivalent to theconceptual prox method -- Clairvoyant OMD. At the same time, we show that ouranalysis yields an improved regret bound compared to the original bound byPiliouras et al., in that the regret of CMWU scales only with the square rootof the number of players, rather than the number of players themselves.

Clairvoyant Regret Minimization: Equivalence with Nemirovski's Conceptual Prox Method and Extension to General Convex Games