Related papers: A Linear Programming Approach to Estimate the Core…
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 $O(T^{-3/4})$…
A solution concept on a class of transferable utility coalitional games is a multifunction satisfying given criteria of economic rationality. Every solution associates a set of payoff allocations with a coalitional game. This general…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
The following four classes of computational problems are equivalent: solving matrix games, solving linear programs, best $l^{\infty}$ linear approximation, best $l^1$ linear approximation.
This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…
In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…
The core is a dominant solution concept in economics and cooperative game theory; it is predominantly used for profit, equivalently cost or utility, sharing. This paper demonstrates the versatility of this notion by proposing a completely…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Two-team zero-sum games are one of the most important paradigms in game theory. In this paper, we focus on finding an unexploitable equilibrium in large team games. An unexploitable equilibrium is a worst-case policy, where members in the…
In cooperative game theory, the primary focus is the equitable allocation of payoffs or costs among agents. However, in the practical applications of cooperative games, accurately representing games is challenging. In such cases, using an…
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
We investigate a routing game that allows for the creation of coalitions, within the framework of cooperative game theory. Specifically, we describe the cost of each coalition as its maximin value. This represents the performance that the…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm…
We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…