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作者：Yu, Di; Henderson, Shane G.; Pasupathy, Raghu
作者单位：Purdue University System; Purdue University; Cornell University
摘要：Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the variational object, we construct a deterministic Frank-Wolfe (dFW) recursion for probability spaces. The dFW recursion is made especially possible by a lemma that identifies the solution to the infinite-dimensional Frank-Wolfe subproblem as a Dirac measure co...
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作者：Necoara, Ion; Fercoq, Olivier
作者单位：National University of Science & Technology POLITEHNICA Bucharest; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
摘要：Our proof of linear convergence for Dykstra's algorithm was erroneous, and in fact, there even exists a counterexample showing that the result is false.
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作者：Necoara, Ion; Chorobura, Flavia
作者单位：National University of Science & Technology POLITEHNICA Bucharest; Romanian Academy
摘要：This paper deals with composite optimization problems having the objective function formed as the sum of two terms; one has a Lipschitz continuous gradient along random subspaces and may be nonconvex, and the second term is simple and differentiable but possibly nonconvex and nonseparable. Under these settings, we design a stochastic coordinate proximal gradient method that takes into account the nonseparable composite form of the objective function. This algorithm achieves scalability by cons...
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作者：Chehrazi, Naveed
作者单位：Washington University (WUSTL)
摘要：We present a continuous -time stochastic model of an inventory system with record inaccuracy. In this formulation, demand is modeled by a point process and is observable only when it leads to sales. In addition to demand that can reduce the stock, an unobservable stochastic loss process can also reduce the stock. The retailer's goal is to identify the restocking and auditing policy that minimizes the expected discounted cost of carrying a product over an infinite horizon. We analytically chara...
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作者：Dong, Youran; Ma, Shiqian; Yang, Tunfeng; Yin, Chao
作者单位：Nanjing University; Rice University; Hohai University
摘要：Bilevel optimization has gained significant attention in recent years because of its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for solving decentralized bilevel optimization with a strongly convex lower-level problem. Our approach is built on the basis of the SOBA framework, and it is a fully single-loop method that approximates the hypergradient by using merely two matrix-vector multi...
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作者：Srikant, R.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We prove a nonasymptotic central limit theorem (CLT) for vector-valued martingale differences using Stein's method, and we use Poisson's equation to extend the result to functions of Markov chains. We then show that these results can be applied to establish a nonasymptotic CLT for temporal difference learning with averaging.
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作者：Portales, Leo; Cazelles, Elsa; Pauwelsc, Edouard
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National Polytechnique de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
摘要：Lloyd's algorithm is an iterative method that solves the quantization problem, that is, the approximation of a target probability measure by a discrete one, and is particularly used in digital applications. This algorithm can be interpreted as a gradient method on a certain quantization functional which is given by optimal transport. We study the sequential convergence (to a single accumulation point) for two variants of Lloyd's method: (i) optimal quantization with an arbitrary discrete measu...
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作者：Babaioff, Moshe; Feige, Uriel
作者单位：Hebrew University of Jerusalem; Weizmann Institute of Science
摘要：We consider fair allocation of indivisible goods to n equally entitled agents. Every agent i has a valuation function vi from some given class of valuation functions. A share s is a function that maps (vi, n) to a nonnegative value. A share is feasible if for every allocation instance, there is an allocation that gives every agent i a bundle that is acceptable with respect to vi, one of value at least her share value s(vi, n). We introduce the following concepts. A share is self-maximizing if ...
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作者：Sharma, Salil; Tsakas, Elias; Voorneveld, Mark
作者单位：Stockholm School of Economics; Maastricht University
摘要：We study settings where information in the form of Bayesian signals is acquired by an expert on behalf of a principal. Information acquisition is costly for the expert and crucially not verifiable by the principal. The expert is compensated by the principal with a menu of state -contingent payments. We provide a full characterization of the set of all menus that implement (respectively, strictly implement) each signal. Moreover, we provide a closed -form characterization for the expected cost ...
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作者：Bonesini, Ofelia; Campi, Luciano; Fischer, Markus
作者单位：Imperial College London; University of Padua; University of Milan
摘要：In a discrete space and time framework, we study the mean field game limit for a class of symmetric N-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows us to construct approximate N-player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions.
