We develop new parameter-free and scale-free algorithms for solving convexconcave saddle-point problems. Our results are based on a new simple regret minimizer, the Conic Blackwell Algorithm+ (CBA+), which attains O(1/ 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, `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-ofthe-art methods on synthetic data and real data instances, without the need for any choice of step sizes or other algorithmic parameters.

In this paper we establish efficient and uncoupled learning dynamics so that, when employed by all players in a general-sum multiplayer game, the swap regret of each player after T repetitions of the game is bounded by O(logT), improving over the prior best bounds of O(log4(T)). At the same time, we guarantee optimal O( T) swap regret in the adversarial regime as well. To obtain these results, our primary contribution is to show that when all players follow our dynamics with a time-invariant learning rate, the second-order path lengths of the dynamics up to time T are bounded by O(logT), a fundamental property which could have further implications beyond near-optimally bounding the (swap) regret. Our proposed learning dynamics combine in a novel way optimistic regularized learning with the use of self-concordant barriers. Further, our analysis is remarkably simple, bypassing the cumbersome framework of higher-order smoothness recently developed by Daskalakis, Fishelson, and Golowich (NeurIPS'21).

A shrinking market is a ubiquitous challenge faced by various industries. In this paper we formulate the first formal model of shrinking markets in multi-item settings, and study how mechanism design and machine learning can help preserve revenue in an uncertain, shrinking market. Via a sample-based learning mechanism, we prove the first guarantees on how much revenue can be preserved by truthful multi-item, multi-bidder auctions (for limited supply) when only a random unknown fraction of the population participates in the market. We first present a general reduction that converts any sufficiently rich auction class into a randomized auction robust to market shrinkage. Our main technique is a novel combinatorial construction called a winner diagram that concisely represents all possible executions of an auction on an uncertain set of bidders. Via a probabilistic analysis of winner diagrams, we derive a general possibility result: a sufficiently rich class of auctions always contains an auction that is robust to market shrinkage and market uncertainty. Our result has applications to important practically-constrained settings such as auctions with a limited number of winners. We then show how to efficiently learn an auction that is robust to market shrinkage by leveraging practically-efficient routines for solving the winner determination problem.

CMWU achieves constant regret ofln(m)/η in all normal-form games with m actions and fixed step-sizesη.

Finally we show that when the goal isminimizing regret, rather than computing a Nash equilibrium, our optimistic methods can outperformCFR+,evenindeepgametrees.

Successfully employing cutting planes can be challenging because there are infinitely many cuts to choose from and there are still many open questions about which cuts to employ when.