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作者：Cohen, Eyal; Teboulle, Marc
作者单位：Tel Aviv University
摘要：There is growing interest in nonconvex minimax problems that is driven by an abundance of applications. Our focus is on nonsmooth, nonconvex-strongly concave minimax, thus departing from the more common weakly convex and smooth models assumed in the recent literature. We present proximal gradient schemes with either parallel or alternating steps. We show that both methods can be analyzed through a single scheme within a unified analysis that relies on expanding a general convergence mechanism ...
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作者：Amarante, Massimiliano; Liebrich, Felix-Benedikt; Munari, Cosimo
作者单位：Universite de Montreal; University of Amsterdam; University of Verona
摘要：We revisit Marinacci's uniqueness theorem for convex -ranged probabilities and its applications. Our approach does away with both the countable additivity and the positivity of the charges involved. In the process, we uncover several new equivalent conditions, which lead to a novel set of applications. These include extensions of the classic Fre ' chet-Hoeffding bounds as well as of the automatic Fatou property of law -invariant functionals. We also generalize existing results of the collapse ...
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作者：Xu, Yunbei; Zeevi, Assaf
作者单位：Columbia University
摘要：We study problem-dependent rates, that is, generalization errors that scale near-optimally with the variance, effective loss, or gradient norms evaluated at the best hypothesis. We introduce a principled framework dubbed uniform localized convergence and characterize sharp problem-dependent rates for central statistical learning problems. From a methodological viewpoint, our framework resolves several fundamental limitations of existing uniform convergence and localization analysis approaches....
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作者：Tang, Wenpin; Yao, David D.
作者单位：Columbia University
摘要：We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof -of -stake protocol. The main idea, inspired by the Penrose square -root law and the more recent quadratic voting rule, is to differentiate a voter's voting power and the voter's share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting power...
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作者：Bertschinger, Nils; Hoefer, Martin; Schmand, Daniel
作者单位：Goethe University Frankfurt; Goethe University Frankfurt; University of Bremen
摘要：We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the chosen allocation strategies evolves in the network. Each agent wants to maximize the amount of flow through his or her node. Flow allocation games can be used to express strate...
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作者：Moharrami, Mehrdad; Murthy, Yashaswini; Roy, Arghyadip; Srikant, R.
作者单位：University of Iowa; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Guwahati
摘要：We study the risk -sensitive exponential cost Markov decision process (MDP) formulation and develop a trajectory -based gradient algorithm to find the stationary point of the cost associated with a set of parameterized policies. We derive a formula that can be used to compute the policy gradient from (state, action, cost) information collected from sample paths of the MDP for each fixed parameterized policy. Unlike the traditional average cost problem, standard stochastic approximation theory ...
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作者：Egea, Maxime; Panloup, Fabien
作者单位：Universite d'Angers; Centre National de la Recherche Scientifique (CNRS)
摘要：We propose and study a new multilevel method for the numerical approximation of a Gibbs distribution pi on Rd, based on (overdamped) Langevin diffusions. This method relies on a multilevel occupation measure, that is, on an appropriate combination of R occupation measures of (constant -step) Euler schemes with respective steps gamma r � gamma 02-r, r � 0,.. .,R. We first state a quantitative result under general assumptions that guarantees an epsilon-approximation (in an L2 -sense) with a co...
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作者：Attia, Luc; Oliu-Barton, Miquel; Saona, Raimundo
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institute of Science & Technology - Austria
摘要：Zero -sum stochastic games are parameterized by payoffs, transitions, and possibly a discount rate. In this article, we study how the main solution concepts, the discounted and undiscounted values, vary when these parameters are perturbed. We focus on the marginal values, introduced by Mills in 1956 in the context of matrix games-that is, the directional derivatives of the value along any fixed perturbation. We provide a formula for the marginal values of a discounted stochastic game. Further,...
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作者：Bellon, Antonio; Henrion, Didier; Kungurtsev, Vyacheslav; Marec, Jakub
作者单位：Czech Technical University Prague; Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose coefficients (input data) depend on a time parameter. We are interested in the geometry of the solution (output data) trajectory, defined as the set of solutions depending on the parameter. We propose an exhaustive description of the geometry of the solution t...
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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...
