Related papers: Reductions Between Expansion Problems
We unify standard frameworks for approachability both in full or partial monitoring by defining a new abstract game, called the "purely informative game", where the outcome at each stage is the maximal information players can obtain,…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
This paper introduces two fundamentally new concepts to game theory: multilateral Nash equilibria and families of games. Starting with non-cooperative games, we show how these notions together seamlessly integrate into and naturally extend…
We introduce a new hypothesis testing-based learning dynamics in which players update their strategies by combining hypothesis testing with utility-driven exploration. In this dynamics, each player forms beliefs about opponents' strategies…
We study a network extension to the Nash bargaining game, as introduced by Kleinberg and Tardos (STOC'08), where the set of players corresponds to vertices in a graph $G=(V,E)$ and each edge $ij\in E$ represents a possible deal between…
We consider $\epsilon$-equilibria notions for constant value of $\epsilon$ in $n$-player $m$-actions games where $m$ is a constant. We focus on the following question: What is the largest grid size over the mixed strategies such that…
Considerable research efforts have recently been made to show that a random neural network $N$ contains subnetworks capable of accurately approximating any given neural network that is sufficiently smaller than $N$, without any training.…
Let be given a graph $G=(V,E)$ whose edge set is partitioned into a set $R$ of \emph{red} edges and a set $B$ of \emph{blue} edges, and assume that red edges are weighted and form a spanning tree of $G$. Then, the \emph{Stackelberg Minimum…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem as well as nonuniform demands such…
In this work, we achieve gap amplification for the Small-Set Expansion problem. Specifically, we show that an instance of the Small-Set Expansion Problem with completeness $\epsilon$ and soundness $\frac{1}{2}$ is at least as difficult as…
The Whitney near extension problem for finite sets in $\mathbb R^d,\, d\geq 2$ asks the following: Let $\phi:E\to \mathbb R^d$ be a near distortion on a finite set $E\subset \mathbb R^d$ with certain geometry. How to decide whether $\phi$…
We reduce the problem of proving a "Boolean Unique Games Conjecture" (with gap 1-delta vs. 1-C*delta, for any C> 1, and sufficiently small delta>0) to the problem of proving a PCP Theorem for a certain non-unique game. In a previous work,…
The main ambition of this thesis is to contribute to the development of cooperative game theory towards combinatorics, algorithmics and discrete geometry. Therefore, the first chapter of this manuscript is devoted to highlighting the…
Partial order reductions have been successfully applied to model checking of concurrent systems and practical applications of the technique show nontrivial reduction in the size of the explored state space. We present a theory of partial…
We prove a theorem computing the number of solutions to a system of equations which is generic subject to the sparsity conditions embodied in a graph. We apply this theorem to games obeying graphical models and to extensive-form games. We…
Recently, invariant risk minimization (IRM) (Arjovsky et al.) was proposed as a promising solution to address out-of-distribution (OOD) generalization. In Ahuja et al., it was shown that solving for the Nash equilibria of a new class of…
We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…
We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel…
This paper argues that the finite horizon paradox, where game theory contradicts intuition, stems from the limitations of standard number systems in modelling the cognitive perception of infinity. To address this issue, we propose a new…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…