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作者：Van Eynde, Rob; Vanhoucke, Mario
作者单位：Ghent University; Vlerick Business School; University of London; University College London
摘要：The resource-constrained project scheduling problem (RCPSP) addresses the problem of constructing a schedule with minimum makespan for a set of activities, subject to precedence and resource constraints. Recent research introduced a data set with small instances that cannot be solved by the state-of-the-art algorithms, revealing a gap in our understanding of instance complexity. We propose a new theoretical framework for the instance complexity for the RCPSP, consecutively incorporating preced...
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作者：Chen, Xi; Chen, Yunxiao; Li, Xiaoou
作者单位：New York University; University of London; London School Economics & Political Science; University of Minnesota System; University of Minnesota Twin Cities
摘要：A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking K items by sequentially collecting noisy pairwise comparisons from judges. The decision maker needs to choose a pair of items for comparison in each step, decide when to stop data collection, and make a final decision after stopping based on a sequential flow of information. Because of the complex ranking structur...
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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...
