arXiv subjects

John Lazarsfeld

Publications and source records attributed to John Lazarsfeld.

11 recordsLinked to original sources

arXiv2026

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.

cs.GT↗

arXiv2026

Optimistic Online Learning in Symmetric Cone Games

We introduce symmetric cone games (SCGs), a broad class of multi-player games where each player's strategy lies in a generalized simplex (the trace-one slice of a symmetric cone). This framework unifies a wide spectrum of settings, including normal-form games (simplex strategies), quantum games (density matrices), and continuous games with ball-constrained strategies. It also captures several structured machine learning and optimization problems, such as distance metric learning and Fermat-Weber facility location, as two-player zero-sum SCGs. To compute approximate Nash equilibria in two-player zero-sum SCGs, we propose a single online learning algorithm: Optimistic Symmetric Cone Multiplicative Weights Updates (OSCMWU). Unlike prior methods tailored to specific geometries, OSCMWU provides closed-form updates over any symmetric cone and achieves a $\tilde{\mathcal{O}}(1/ε)$ iteration complexity for computing $ε$-saddle points. Our analysis builds on the Optimistic Follow-the-Regularized-Leader framework and hinges on a key technical contribution: We prove that the symmetric cone negative entropy is strongly convex with respect to the trace-one norm. This result extends known results for the simplex and spectraplex to all symmetric cones, and may be of independent interest.

math.OC↗

arXiv2026

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.

cs.LG↗

arXiv2025

Online Multi-Agent Control with Adversarial Disturbances

Online multi-agent control problems, where many agents pursue competing and time-varying objectives, are widespread in domains such as autonomous robotics, economics, and energy systems. In these settings, robustness to adversarial disturbances is critical. In this paper, we study online control in multi-agent linear dynamical systems subject to such disturbances. In contrast to most prior work in multi-agent control, which typically assumes noiseless or stochastically perturbed dynamics, we consider an online setting where disturbances can be adversarial, and where each agent seeks to minimize its own sequence of convex losses. Under two feedback models, we analyze online gradient-based controllers with local policy updates. We prove per-agent regret bounds that are sublinear and near-optimal in the time horizon and that highlight different scalings with the number of agents. When agents' objectives are aligned, we further show that the multi-agent control problem induces a time-varying potential game for which we derive equilibrium tracking guarantees. Together, our results take a first step in bridging online control with online learning in games, establishing robust individual and collective performance guarantees in dynamic continuous-state environments.

cs.LG↗

arXiv2025

Fast and Furious Symmetric Learning in Zero-Sum Games: Gradient Descent as Fictitious Play

This paper investigates the sublinear regret guarantees of two non-no-regret algorithms in zero-sum games: Fictitious Play, and Online Gradient Descent with constant stepsizes. In general adversarial online learning settings, both algorithms may exhibit instability and linear regret due to no regularization (Fictitious Play) or small amounts of regularization (Gradient Descent). However, their ability to obtain tighter regret bounds in two-player zero-sum games is less understood. In this work, we obtain strong new regret guarantees for both algorithms on a class of symmetric zero-sum games that generalize the classic three-strategy Rock-Paper-Scissors to a weighted, n-dimensional regime. Under symmetric initializations of the players' strategies, we prove that Fictitious Play with any tiebreaking rule has $O(\sqrt{T})$ regret, establishing a new class of games for which Karlin's Fictitious Play conjecture holds. Moreover, by leveraging a connection between the geometry of the iterates of Fictitious Play and Gradient Descent in the dual space of payoff vectors, we prove that Gradient Descent, for almost all symmetric initializations, obtains a similar $O(\sqrt{T})$ regret bound when its stepsize is a sufficiently large constant. For Gradient Descent, this establishes the first "fast and furious" behavior (i.e., sublinear regret without time-vanishing stepsizes) for zero-sum games larger than 2x2.

cs.LG↗

arXiv2024

Simple Opinion Dynamics for No-Regret Learning

We study a cooperative multi-agent bandit setting in the distributed GOSSIP model: in every round, each of $n$ agents chooses an action from a common set, observes the action's corresponding reward, and subsequently exchanges information with a single randomly chosen neighbor, which may inform its choice in the next round. We introduce and analyze families of memoryless and time-independent protocols for this setting, inspired by opinion dynamics that are well-studied for other algorithmic tasks in the GOSSIP model. For stationary reward settings, we prove for the first time that these simple protocols exhibit best-of-both-worlds behavior, simultaneously obtaining constant cumulative regret scaling like $R(T)/T = \widetilde O(1/T)$, and also reaching consensus on the highest-mean action within $\widetilde O(\sqrt{n})$ rounds. We obtain these results by showing a new connection between the global evolution of these decentralized protocols and a class of zero-sum multiplicative weights update} processes. Using this connection, we establish a general framework for analyzing the population-level regret and other properties of our protocols. Finally, we show our protocols are also surprisingly robust to adversarial rewards, and in this regime we obtain sublinear regret scaling like $R(T)/T = \widetilde O(1/\sqrt{T})$ as long as the number of rounds does not grow too fast as a function of $n$.

cs.LG↗

arXiv2024

Game Dynamics and Equilibrium Computation in the Population Protocol Model

We initiate the study of game dynamics in the population protocol model: $n$ agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a payoff from an underlying utility function, and they can subsequently update their strategies according to a fixed local algorithm. In this setting, we ask how the distribution over agent strategies evolves over a sequence of interactions, and we introduce a new distributional equilibrium concept to quantify the quality of such distributions. As an initial example, we study a class of repeated prisoner's dilemma games, and we consider a family of simple local update algorithms that yield non-trivial dynamics over the distribution of agent strategies. We show that these dynamics are related to a new class of high-dimensional Ehrenfest random walks, and we derive exact characterizations of their stationary distributions, bounds on their mixing times, and prove their convergence to approximate distributional equilibria. Our results highlight trade-offs between the local state space of each agent, and the convergence rate and approximation factor of the underlying dynamics. Our approach opens the door towards the further characterization of equilibrium computation for other classes of games and dynamics in the population setting.

cs.DC↗

arXiv2023

Approximate Majority With Catalytic Inputs

Population protocols are a class of algorithms for modeling distributed computation in networks of finite-state agents communicating through pairwise interactions. Their suitability for analyzing numerous chemical processes has motivated the adaptation of the original population protocol framework to better model these chemical systems. In this paper, we further the study of two such adaptations in the context of solving approximate majority: persistent-state agents (or catalysts) and spontaneous state changes (or leaks). Based on models considered in recent protocols for populations with persistent-state agents, we assume a population with $n$ catalytic input agents and $m$ worker agents, and the goal of the worker agents is to compute some predicate over the states of the catalytic inputs. We call this model the Catalytic Input (CI) model. For $m = Θ(n)$, we show that computing the exact majority of the input population with high probability requires at least $Ω(n^2)$ total interactions, demonstrating a strong separation between the CI model and the standard population protocol model. On the other hand, we show that the simple third-state dynamics of Angluin et al. for approximate majority in the standard model can be naturally adapted to the CI model: we present such a constant-state protocol for the CI model that solves approximate majority in $O(n \log n)$ total steps w.h.p. when the input margin is $Ω(\sqrt{n \log n})$. We then show the robustness of third-state dynamics protocols to the transient leaks events introduced by Alistarh et al. In both the original and CI models, these protocols successfully compute approximate majority with high probability in the presence of leaks occurring at each step with probability $β\leq O\left(\sqrt{n \log n}/n\right)$, exhibiting a resilience to leaks similar to that of Byzantine agents in previous works.

cs.DC↗

arXiv2023

Fast Convergence of $k$-Opinion Undecided State Dynamics in the Population Protocol Model

We analyze the convergence of the $k$-opinion Undecided State Dynamics (USD) in the population protocol model. For $k$=2 opinions it is well known that the USD reaches consensus with high probability within $O(n \log n)$ interactions. Proving that the process also quickly solves the consensus problem for $k>2$ opinions has remained open, despite analogous results for larger $k$ in the related parallel gossip model. In this paper we prove such convergence: under mild assumptions on $k$ and on the initial number of undecided agents we prove that the USD achieves plurality consensus within $O(k n \log n)$ interactions with high probability, regardless of the initial bias. Moreover, if there is an initial additive bias of at least $Ω(\sqrt{n} \log n)$ we prove that the initial plurality opinion wins with high probability, and if there is a multiplicative bias the convergence time is further improved. Note that this is the first result for $k > 2$ for the USD in the population protocol model. Furthermore, it is the first result for the unsynchronized variant of the USD with $k>2$ which does not need any initial bias.

cs.DC↗

arXiv2022

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.

cs.CR↗

arXiv2021

Consistency of the Maximal Information Coefficient Estimator

The Maximal Information Coefficient (MIC) of Reshef et al. (Science, 2011) is a statistic for measuring dependence between variable pairs in large datasets. In this note, we prove that MIC is a consistent estimator of the corresponding population statistic MIC$_*$. This corrects an error in an argument of Reshef et al. (JMLR, 2016), which we describe.

stat.ME↗