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John Lazarsfeld

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Machine Learning Computer Science and Game Theory Cryptography and Security Information Theory math.IT Methodology

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preprint2026arXiv

Optimism Without Regularization: Constant Regret in Zero-Sum Games

This paper studies the optimistic variant of Fictitious Play for learning in two-player zero-sum games. While it is known that Optimistic FTRL -- a regularized algorithm with a bounded stepsize parameter -- obtains constant regret in this setting, we show for the first time that similar, optimal rates are also achievable without regularization: we prove for two-strategy games that Optimistic Fictitious Play (using any tiebreaking rule) obtains only constant regret, providing surprising new evidence on the ability of non-no-regret algorithms for fast learning in games. Our proof technique leverages a geometric view of Optimistic Fictitious Play in the dual space of payoff vectors, where we show a certain energy function of the iterates remains bounded over time. Additionally, we also prove a regret lower bound of $Ω(\sqrt{T})$ for Alternating Fictitious Play. In the unregularized regime, this separates the ability of optimism and alternation in achieving $o(\sqrt{T})$ regret.

preprint2026arXiv

When and Why is Optimistic Multiplicative Weights Slow? The Geometry of Energy Dissipation

This paper studies the convergence of the Optimistic Multiplicative Weights Update algorithm (OMWU) in two player zero-sum games. Recent works have identified instances on which the last-iterate of OMWU can converge arbitrarily slowly, but understanding when and why this slow convergence occurs has remained open. In this work, we develop a new analysis framework that gives sharp, quantitative explanations for this behavior. Our analysis is based on viewing the algorithm's dual iterates as an optimistic skew-gradient descent with respect to an energy function. We prove over the dual iterates that energy is dissipative, and by establishing tight bounds on the magnitude of dissipation, our analysis quantifies the geometric bottlenecks that arise when the corresponding primal iterates are close to the simplex boundary. This further translates into a new linear last-iterate convergence rate in KL divergence on games with a unique and interior Nash equilibrium. Compared to prior work, this new rate contains a much sharper dependence on game-specific constants, and we prove this dependence is optimal. Moreover, these geometric insights further translate into new separations on uniform convergence rates for OMWU. On the one hand, we prove constant lower bounds on the uniform best-iterate convergence rate in KL divergence and total variation distance from Nash. On the other hand, we establish for the $2\times 2$ setting a new ${\widetilde O}(T^{-1/2})$ best-iterate rate in duality gap, improving substantially over prior work. Together, this shows in general that uniform convergence rate guarantees do not transfer across different measures of distance to Nash.

preprint2022arXiv

Differentially Private Maximal Information Coefficients

The Maximal Information Coefficient (MIC) is a powerful statistic to identify dependencies between variables. However, it may be applied to sensitive data, and publishing it could leak private information. As a solution, we present algorithms to approximate MIC in a way that provides differential privacy. We show that the natural application of the classic Laplace mechanism yields insufficient accuracy. We therefore introduce the MICr statistic, which is a new MIC approximation that is more compatible with differential privacy. We prove MICr is a consistent estimator for MIC, and we provide two differentially private versions of it. We perform experiments on a variety of real and synthetic datasets. The results show that the private MICr statistics significantly outperform direct application of the Laplace mechanism. Moreover, experiments on real-world datasets show accuracy that is usable when the sample size is at least moderately large.