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作者：Garnier, Guillaume; Ziliotto, Bruno
作者单位：Universite Paris Cite; Inria; Sorbonne Universite; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper introduces a discrete-time stochastic game class on Zd, which plays the role of a toy model for the well-known problem of stochastic homogenization of Hamilton-Jacobi equations. Conditions are provided under which the n-stage game value converges as n tends to infinity, and connections with homogenization theory are discussed.
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作者：Ghossoub, Mario; Hall, Jesse; Saunders, David
作者单位：University of Waterloo
摘要：We consider the problemof determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known but whose joint distribution is unknown. The factors may take values in complete separable metric spaces. We introduce the notion of Maximum Spectral Measure (MSM), as a worst-case spectral risk measure of the loss with respect to the dependence between the factors. The MSM admits a formulation as a so...
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作者：Na, Sen; Anitescu, Mihai; Kolar, Mladen
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; United States Department of Energy (DOE); Argonne National Laboratory; University of Chicago
摘要：We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap...
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作者：Bartl, Daniel; Tangpi, Ludovic
作者单位：University of Vienna; Princeton University
摘要：Let rho be a general law-invariant convex risk measure, for instance, the average value at risk, and let X be a financial loss, that is, a real random variable. In practice, either the true distribution mu of X is unknown, or the numerical computation of rho(mu) is not possible. In both cases, either relying on historical data or using a Monte Carlo approach, one can resort to an independent and identically distributed sample of mu to approximate rho(mu) by the finite sample estimator rho(mu N...
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作者：Friedlander, Michael P.; Goodwin, Ariel; Hoheisel, Tim
作者单位：University of British Columbia; McGill University
摘要：The projection onto the epigraph or a level set of a closed proper convex function can be achieved by finding a root of a scalar equation that involves the proximal operator as a function of the proximal parameter. This paper develops the variational analysis of this scalar equation. The approach is based on a study of the variational-analytic properties of general convex optimization problems that are (partial) infimal projections of the sum of the function in question and the perspective map...
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作者：Dianetti, Jodi; Ferrari, Giorgio; Fischer, Markus; Nendel, Max
作者单位：University of Bielefeld; University of Padua
摘要：We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow us to prove the existence and approximation of strong mean field equilibria in models where data may not be continuous with respect to the measure parameter and common noise is allowed. The setting is general enough to encompass qualitatively different problems, such as mean field games for discrete time finite space Markov chains, singularly controlled and reflected diffus...
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作者：Gao, Rui; Kleywegt, Anton
作者单位：University of Texas System; University of Texas Austin; University System of Georgia; Georgia Institute of Technology
摘要：Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of distributions. In this paper, we first point out that the set of distributions should be chosen to be appropriate for the application at hand and some of the choices that have been popular until recently are, for many applications, not good choices. We next conside...
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作者：Mahara, Ryoga
作者单位：University of Tokyo
摘要：Envy freeness is one of the most widely studied notions in fair division. Because envy-free allocations do not always exist when items are indivisible, several relaxations have been considered. Among them, possibly the most compelling notion is envy freeness up to any item (EFX). Informally speaking, EFX requires that no agent i envies another agent j after the removal of any item in j's bundle. The existence of EFX allocations is a major open problem. We study the existence of EFX allocations...
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作者：Liu, Kang; Oudjane, Nadia; Wan, Cheng
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Institut Polytechnique de Paris; ENSTA Paris
摘要：This paper shows the existence of O(1/n(gamma))-Nash equilibria in n-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players' actions, are lower semicontinuous in the former, whereas gamma-Holder continuous in the latter. Neither the action sets nor the cost functions need to be convex. For an important class of sum-aggregative games, which includes congestion games with gamma equal to one, a gradient-p...
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作者：Cominetti, Roberto; Scarsini, Marco; Schroder, Marc; Stier-Moses, Nicolas
作者单位：Universidad Adolfo Ibanez; Luiss Guido Carli University; Maastricht University
摘要：We consider the question of whether and in what sense, Wardrop equilibria provide a good approximation for Nash equilibria in atomic unsplittable congestion games with a large number of small players. We examine two different definitions of small players. In the first setting, we consider games in which each player's weight is small. We prove that when the number of players goes to infinity and their weights to zero, the random flows in all (mixed) Nash equilibria for the finite games converge...
