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• A Variable Sample-Size Stochastic Quasi-Newton Method for Smooth and Nonsmooth Stochastic Convex Optimization AI翻译
  作者：Jalilzadeh, Afrooz; Nedic, Angelia; Shanbhag, Uday, V; Yousefian, Farzad
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Arizona State University; Arizona State University-Tempe; Oklahoma State University System; Oklahoma State University - Stillwater
  摘要：Classical theory for quasi-Newton schemes has focused on smooth, deterministic, unconstrained optimization, whereas recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes. Naturally, there is a compelling need to address nonsmoothness, the lack of strong convexity, and the presence of constraints. Accordingly, this paper presents a quasi-Newton framework that can process merely convex and possibly nonsmooth (but smoothable) ...
• Variational Analysis of Composite Models with Applications to Continuous Optimization AI翻译
  作者：Mohammadi, Ashkan; Mordukhovich, Boris S.; Sarabi, M. Ebrahim
  作者单位：Wayne State University; University System of Ohio; Miami University
  摘要：The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate. The underlying theme of our study is a systematical replacement of conventional metric regularity and related requirements by much weaker metric subregulatity ones that lead us to significantly stronger and completely new results of first-order and second-ord...
• Graphical Convergence of Subgradients in Nonconvex Optimization and Learning AI翻译
  作者：Davis, Damek; Drusvyatskiy, Dmitriy
  作者单位：Cornell University; University of Washington; University of Washington Seattle
  摘要：We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such losses. We analyze the estimation quality of such nonsmooth and nonconvex problems by their sample average approximations. Our main results establish dimension-dependent rates on subgradient estimation in full generality and dimension-independent rates when ...
• Discrete Choice Prox-Functions on the Simplex AI翻译
  作者：Mueller, David; Nesterov, Yurii; Shikhman, Vladimir
  作者单位：Technische Universitat Chemnitz; Universite Catholique Louvain
  摘要：We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to a probabilistic interpretations of the iteration steps...
• Finite-Memory Strategies in POMDPs with Long-Run Average Objectives AI翻译
  作者：Chatterjee, Krishnendu; Saona, Raimundo; Ziliotto, Bruno
  作者单位：Institute of Science & Technology - Austria; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
  摘要：Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function.
• Hamilton-Jacobi Equations with Semilinear Costs and State Constraints, with Applications to Large Deviations in Games AI翻译
  作者：Sandholm, William H.; Tran, Hung, V; Arigapudi, Srinivas
  作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
  摘要：We characterize solutions of a class of time-homogeneous optimal control problems with semilinear running costs and state constraints as maximal viscosity sub-solutions to Hamilton-Jacobi equations and show that optimal solutions to these problems can be constructed explicitly. We present applications to large deviations problems arising in evolutionary game theory.
• Polyhedral Clinching Auctions for Two-Sided Markets AI翻译
  作者：Hirai, Hiroshi; Sato, Ryosuke
  作者单位：University of Tokyo
  摘要：In this paper, we present a new model and mechanisms for auctions in two-sided markets of buyers and sellers, where budget constraints are imposed on buyers. Our model incorporates polymatroidal environments and is applicable to a variety of models that include multiunit auctions, matching markets, and reservation exchange markets. Our mechanisms are built on the polymatroidal network flow model by Lawler and Martel. Additionally, they feature nice properties such as the incentive compatibilit...
• Mean Field Analysis of Deep Neural Networks AI翻译
  作者：Sirignano, Justin; Spiliopoulos, Konstantinos
  作者单位：University of Oxford; Boston University
  摘要：We analyze multilayer neural networks in the asymptotic regime of simultaneously (a) large network sizes and (b) large numbers of stochastic gradient descent training iterations. We rigorously establish the limiting behavior of the multilayer neural network output. The limit procedure is valid for any number of hidden layers, and it naturally also describes the limiting behavior of the training loss. The ideas that we explore are to (a) take the limits of each hidden layer sequentially and (b)...
• Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients AI翻译
  作者：Djehiche, Boualem; Hamadene, Said; Hdhiri, Ibtissem; Zaatra, Helmi
  作者单位：Royal Institute of Technology; Le Mans Universite; Universite de Gabes
  摘要：We study a class of infinite horizon impulse control problems with execution delay when the dynamics of the system is described by a general stochastic process adapted to the Brownian filtration. The problem is solved by means of probabilistic tools relying on the notion of Snell envelope and infinite horizon reflected backward stochastic differential equations. This allows us to establish the existence of an optimal strategy over all admissible strategies.
• Computation of Dynamic Equilibria in Series-Parallel Networks AI翻译
  作者：Kaiser, Marcus
  作者单位：Technical University of Munich
  摘要：We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a dynamic equilibrium, every infinitesimally small flow particle reaches the sink as early as possible given the pattern of the rest of the flow. Although this model has been examined for many decades, progress has been relatively recent. In particular, the deri...