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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)...
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作者：Rios-Zertuche, Rodolfo
作者单位：Centre National de la Recherche Scientifique (CNRS)
摘要：We show that the vanishing step size subgradient method-widely adopted for machine learning applications-can display rather messy behavior even in the presence of favorable assumptions. We establish that convergence of bounded subgradient sequences may fail even with a Whitney stratifiable objective function satisfying the Kurdyka-Lojasiewicz inequality. Moreover, when the objective function is path-differentiable, we show that various properties all may fail to occur: criticality of the limit...
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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.
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作者：Duvocelle, Benoit; Mertikopoulos, Panayotis; Staudigl, Mathias; Vermeulen, Dries
作者单位：Maastricht University; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; Maastricht University
摘要：We examine the long-run behavior of multiagent online learning in games that evolve over time. Specifically, we focus on a wide class of policies based on mirror descent, and we show that the induced sequence of play (a) converges to a Nash equilibrium in time-varying games that stabilize in the long run to a strictly monotone limit, and (b) it stays asymptotically close to the evolving equilibrium of the sequence of stage games (assuming they are strongly monotone). Our results apply to both ...
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作者：Zheng, Xi Yin
作者单位：Yunnan University
摘要：Noting that the existing Slater condition, as a fundamental constraint qualification in optimization, is only applicable in the convex setting, we introduce and study the Slater condition for the Bouligand and Clarke tangent derivatives of a general vector-valued function F with respect to a closed convex cone K. Without any assumption, it is proved that the Slater condition for the Clarke (respectively, Bouligand) tangent derivative with respect to K is always stable when the objective functi...
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作者：Joswig, Michael; Schroter, Benjamin
作者单位：Technical University of Berlin; Max Planck Society; Royal Institute of Technology
摘要：We study parameterized versions of classical algorithms for computing shortest-path laces. This is most easily expressed in terms of tropical geometry. Applications include shortest paths in traffic networks with variable link travel times.
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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...
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作者：He, Xue Dong; Jiang, Zhaoli
作者单位：Chinese University of Hong Kong
摘要：In a market that consists of multiple stocks and one risk-free asset whose mean return rates and volatility are deterministic, we study a continuous-time mean-variance portfolio selection problem in which an agent is subject to a constraint that the expectation of the agent's terminal wealth must exceed a target and minimize the variance of the agent's terminal wealth. The agent can revise the expected terminal wealth target dynamically to adapt to the change of the agent's current wealth, and...
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作者：Jungnitsch, Karsten; Peis, Britta; Schroder, Marc
作者单位：RWTH Aachen University; Maastricht University
摘要：In a Stackelberg max closure game, we are given a digraph whose vertices correspond to projects from which firms can choose and whose arcs represent precedence constraints. Some projects are under the control of a leader who sets prices in the first stage of the game, while in the second stage, the firms choose a feasible subset of projects of maximum value. For a single follower, the leader's problem of finding revenue-maximizing prices can be solved in strongly polynomial time. In this paper...
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作者：Quoc Tran-Dinh; Liang, Ling; Toh, Kim-Chuan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; National University of Singapore; National University of Singapore
摘要：This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is to utilize a new parameterization strategy of the optimality condition to design a class of homotopy proximal variable-metric algorithms that can achieve linear convergence and finite global iteration-complexity bounds. We identify at least three subclasses of convex problems in which our approach can apply to achieve linear conver...
