Neural Information Processing Systems http://nips.cc/

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.

Neural Information Processing Systems http://nips.cc/

A.1 Proof of proposition 4.1 (See page 4) A.2 Proof of proposition 4.2 (See page 4) MTOs in the form of Equation ( 9) are consistent and exchangeable. MTO s are consistent and exchangeable for the general form. These convex functions are then randomly shifted and rescaled to increase diversity. To circumvent memory issues, we use deep sets in this instance. Note that we do not share parameters among iterations.

Neural Information Processing Systems http://nips.cc/

We sincerely appreciate the time and the efforts the reviewers invested in reading our paper and providing valuable1 feedback. We illustrated the usefulness of our framework on3 the sampling problem and obtained a significantly better result than numerous previous results without making any4 extra assumptions. We believe that there are many other applications of our framework and that our paper is among5 thetopacceptedpapers.6 To Reviewer 1: Thanks for the citations and the correction you provided. To Reviewer 2: The problem studied in our paper, sampling from log-concave distributions, is an essential tool for12 Bayesian inference. It also has many other applications such as volume computation and bandit optimization.