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最新文章

• Optimal Investment Strategy for a-Robust Utility Maximization Problem AI翻译
  作者：Yang, Zhou; Li, Danping; Zeng, Yan; Liu, Guanting
  作者单位：South China Normal University; East China Normal University; Sun Yat Sen University; University of New South Wales Sydney
  摘要：In reality, investors are uncertain about the dynamics of risky asset returns. Therefore, investors prefer to make robust investment decisions. In this paper, we propose an alpha-robust utility maximization problem under uncertain parameters. The investor is allowed to invest in a financial market consisting of a risk -free asset and a risky asset. The uncertainty about the expected return rate is parameterized by a nonempty set. Different from most existing literature on robust utility maximi...
• Convergence and Stability of Coupled Belief-Strategy Learning Dynamics in Continuous Games AI翻译
  作者：Wu, Manxi; Amin, Saurabh; Ozdaglar, Asuman
  作者单位：Cornell University; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
  摘要：We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoffrelevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players' strategies and realized payoffs using Bayes' rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the ...
• A Characterization of Simultaneous Optimization, Majorization, and (Bi-)Submodular Polyhedra AI翻译
  作者：Uiterkamp, Martijn H. H. Schoot
  作者单位：Tilburg University
  摘要：Motivated by resource allocation problems (RAPs) in power management applications, we investigate the existence of solutions to optimization problems that simultaneously minimize the class of Schur-convex functions, also called least-majorized elements. For this, we introduce a generalization of majorization and least-majorized elements, called (a, b)-majorization and least (a, b)-majorized elements, and characterize the feasible sets of problems that have such elements in terms of base and (b...
• Strongly Convergent Homogeneous Approximations to Inhomogeneous Markov Jump Processes and Applications AI翻译
  作者：Bladt, Martin; Peraltab, Oscar
  作者单位：University of Copenhagen; Cornell University
  摘要：The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial mathematical burden which is usually circumvented by using well-known generic distributional approximations or simulations. This article provides a novel approximation method that tailors the dynamics of a time-homogeneous Markov jump process to meet those of its tim...
• Sample-Path Large Deviations for Unbounded Additive Functionals of the Reflected Random Walk AI翻译
  作者：Bazhba, Mihail; Blanchet, Jose; Rhee, Chang-Han; Zwart, Bert
  作者单位：University of Amsterdam; Stanford University; Northwestern University; Eindhoven University of Technology
  摘要：We prove a sample -path large deviation principle (LDP) with sublinear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space D[0, 1] equipped with the M ' 1 topology. Our technique hinges on a suitable decomposition of the Markov chain in terms of regeneration cycles. Each regeneration cycle denotes the area accumulated during the busy period of the reflected random walk. We prove a large deviation principle for the area...
• Fast Rates for the Regret of Offline Reinforcement Learning AI翻译
  作者：Hu, Yichun; Kallus, Nathan; Uehara, Masatoshi
  作者单位：Cornell University
  摘要：We study the regret of offline reinforcement learning in an infinite -horizon discounted Markov decision process (MDP). While existing analyses of common approaches, such as fitted Q -iteration (FQI), suggest root -n convergence for regret, empirical behavior exhibits much faster convergence. In this paper, we present a finer regret analysis that exactly characterizes this phenomenon by providing fast rates for the regret convergence. First, we show that given any estimate for the optimal qual...
• Submodular Functions and Perfect Graphs AI翻译
  作者：Abrishami, Tara; Chudnovsky, Maria; Dibek, Cemil; Vuskovic, Kristina
  作者单位：University of Hamburg; Princeton University; Princeton University; University of Leeds
  摘要：We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph. An even pair in a graph is a pair of vertices all induced paths between which are even. An even set is a set of vertices every two of which are an even pair. We show that every perfect graph that does not contain a prism or a hole of length four as an induced subgraph has a balanced separator ...
• Scheduling in the High-Uncertainty Heavy Traffic Regime AI翻译
  作者：Atar, Rami; Castiel, Eyal; Shadmi, Yonatan
  摘要：We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual diffusion scale as opposed to asymptotically vanishing disturbances studied previously in relation to heavy traffic. A main advantage of the approach is that the invariance principle underlying diffusion limits makes it possible to define uncertainty classes in ter...
• Stationary Points of a Shallow Neural Network with Quadratic Activations and the Global Optimality of the Gradient Descent Algorithm AI翻译
  作者：Gamarnik, David; Kizildag, Eren C.; Zadik, Ilias
  作者单位：Massachusetts Institute of Technology (MIT); Columbia University; Yale University
  摘要：We consider the problem of training a shallow neural network with quadratic activation functions and the generalization power of such trained networks. Assuming that the samples are generated by a full rank matrix W* of the hidden network node weights, we obtain the following results. We establish that all full -rank approximately stationary solutions of the risk minimization problem are also approximate global optimums of the risk (in -sample and population). As a consequence, we establish th...
• Risk Sharing with Lambda Value at Risk AI翻译
  作者：Liu, Peng
  作者单位：University of Essex
  摘要：In this paper, we study the risk-sharing problem among multiple agents using lambda value at risk (AVaR) as their preferences via the tool of inf-convolution, where AVaR is an extension of value at risk (VaR). We obtain explicit formulas of the infconvolution of multiple AVaR with monotone A and explicit forms of the corresponding optimal allocations, extending the results of the inf-convolution of VaR. It turns out that the inf-convolution of several AVaR is still a AVaR under some mild condi...