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Two of the most prominent algorithms for solving unconstrained smooth games are the classical stochastic gradient descent-ascent (SGDA) and the recently introduced stochastic consensus optimization (SCO) [Mescheder et al., 2017]. SGDA is…
In the Max-k-diameter problem, we are given a set of points in a metric space, and the goal is to partition the input points into k parts such that the maximum pairwise distance between points in the same part of the partition is minimized.…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
The existential k-pebble game characterizes the expressive power of the existential-positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given finite structures can be…
We study policy optimization algorithms for computing correlated equilibria in multi-player general-sum Markov Games. Previous results achieve $O(T^{-1/2})$ convergence rate to a correlated equilibrium and an accelerated $O(T^{-3/4})$…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…
Hardness results for maximum agreement problems have close connections to hardness results for proper learning in computational learning theory. In this paper we prove two hardness results for the problem of finding a low degree polynomial…
This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell…
We give a 2-approximation algorithm for Non-Uniform Sparsest Cut that runs in time $n^{O(k)}$, where $k$ is the treewidth of the graph. This improves on the previous $2^{2^k}$-approximation in time $\poly(n) 2^{O(k)}$ due to Chlamt\'a\v{c}…
Stackelberg games have been widely used to model interactive decision-making problems in a variety of domains such as energy systems, transportation, cybersecurity, and human-robot interaction. However, existing algorithms for solving…
Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…
Winning sets of Schmidt's game enjoy a remarkable rigidity. Therefore, this game (and modifications of it) have been applied to many examples of complete metric spaces (X, d) to show that the set of "badly approximable points", with respect…
This article explores the minimum approximation ratio for Nash equilibrium in bi-matrix games, focusing on the Tsaknakis and Spirakis (TS) methods. The previous SOTA, TS algorithm, achieved an approximation ratio of 0.3393, but efforts to…
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…
In this paper, we study the weighted $k$-server problem on the uniform metric in both the offline and online settings. We start with the offline setting. In contrast to the (unweighted) $k$-server problem which has a polynomial-time…
We study the approximability of the NP-complete \textsc{Maximum Minimal Feedback Vertex Set} problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type:…
Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…
We study the problem of finding optimal correlated equilibria of various sorts in extensive-form games: normal-form coarse correlated equilibrium (NFCCE), extensive-form coarse correlated equilibrium (EFCCE), and extensive-form correlated…
We initiate the systematic study of a recently introduced polynomial-time analogue of MaxSNP, which includes a large number of well-studied problems (including Nearest and Furthest Neighbor in the Hamming metric, Maximum Inner Product,…