Zero-sum games can be solved using online learning dynamics, where a classical technique involves simulating two no-regret algorithms that play against each other and, afterT rounds, the average iterate is guaranteed to solve the original optimization problem with error decaying asO(logT/T). In this paper we show that the technique can be enhanced to a rate ofO(1/T2) by extending recent work [22, 25] that leverages optimistic learning to speed upequilibrium computation.

Various theoretical results provideupper bounds onthedistance between the target and marginal distribution after a fixed number of iterations.

Shift-and-invert preconditioning, as a classic acceleration technique for the leading eigenvector computation, has received much attention again recently, owing to fast least-squares solvers for efficiently approximating matrix inversions in power iterations.

However,theanalysis ofsuchdataposes challenges due to the high levels of noise, sparsity, and data scale encountered.

Seide 23] and 25] were reduce accumulation.

Most of this work was done when Fanghui was at KULeuven.

We study a distributionally robust mean square error estimation problem over a nonconvexWasserstein ambiguity set containing only normal distributions.

We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent Ascent (OGDA).

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In addition to solving (1), we also wish topreserve privacyfor the people who contributed to the dataset Z.