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作者：Tabri, Rami
作者单位：Monash University
摘要：Relative entropy minimization is a widely used method in decisions and operations research that incorporates information through constraints on the underlying probability model. The solution is called information projection, and we present new results for its existence, exponential family representation, and approximation in the infinite-dimensional setting for moment inequality constraint sets, nesting both conditional and unconditional moments and allowing for an infinite number of such ineq...
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作者：Semirat, Stephan; Forges, Francoise
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Centre National de la Recherche Scientifique (CNRS); Institut de Recherche pour le Developpement (IRD); Universite PSL; Laboratoire dEconomie de Dauphine LEDa; Universite Paris-Dauphine
摘要：We consider information transmission between a sender, who has finitely many types, and a receiver, who must choose a decision in a real interval. The payoffs depend on the sender's type and the receiver's decision. We assume that the payoff functions are wellbehaved. We characterize the pure strategy perfect Bayesian equilibrium outcomes as incentive-compatible partitions of the sender's types. We propose an algorithm, which starts from the finest partition. Then, at every step, if the curren...
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作者：Hajiabolhassan, Hossein; Ortner, Ronald
作者单位：Medical University of Graz; University of Leoben
摘要：We consider general reinforcement learning under the average reward criterion in Markov decision processes (MDPs), when the learner's goal is not to learn an optimal policy, but accepts any policy whose average reward is above a given satisfaction level a. We show that with this more modest objective, it is possible to give algorithms that only have constant regret with respect to the level a, provided that there is a policy above this level. This is a generalization of known results from the ...
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作者：Fujishie, Satoru; Yang, Zaifu
作者单位：Kyoto University; University of York - UK
摘要：We propose a novel strategy-proof dynamic auction for efficiently allocating heterogeneous indivisible commodities. The auction applies to all unimodular demand types of Baldwin and Klemperer's necessary and sufficient condition for the existence of competitive equilibrium which accommodate a wide variety of complements, substitutes, gross substitutes and complements, and any other kinds. Although bidders are not assumed to be price takers so they can act strategically, this auction induces bi...
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作者：Brustle, Johannes; Correa, Jose; Dutting, Paul; Ezra, Tomer; Feldman, Michal; Verdugo, Victor
作者单位：Sapienza University Rome; Universidad de Chile; Harvard University; Tel Aviv University; Pontificia Universidad Catolica de Chile; Pontificia Universidad Catolica de Chile
摘要：We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the (1- E)-competition complexity of different types of online algorithms. This metric asks for the smallest k such that the expected value of the online algorithm on k copies of the original instance is at least a (1 - E)-approximation to the expected off-line optimum on a single copy. We show that block threshold algorithms, which set one threshold per copy, are optimal an...
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作者：Hu, Chunhai; Yao, Wei; Zhang, Jin
作者单位：Yunnan University of Finance & Economics; Southern University of Science & Technology; Southern University of Science & Technology; Southern University of Science & Technology
摘要：This paper introduces a decomposition method to analyze the Lipschitz stability of solution mappings for general least absolute shrinkage and selection operator-type (LASSO-type) problems with convex data fidelity and L1-regularization terms. The solution mappings are considered as set-valued mappings of the measurement vector and the regularization parameter. Based on the proposed method, we establish two regularity conditions for Lipschitz stability: a weak condition and a strong condition. ...
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作者：Guo, Feng
作者单位：Dalian University of Technology
摘要：This paper establishes new Positivstellensa & uml;tze for polynomials that are positive on sets defined by polynomial matrix inequalities (PMIs). We extend the classical Handelman and Krivine-Stengle theorems from the scalar inequality setting to the matrix context, deriving explicit certificate forms that do not rely on sums of squares (SOS). Specifically, we show that under certain conditions, any polynomial positive on a PMI-defined semialgebraic set admits a representation using Kronecker ...
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作者：Hu, Yaohua; Wang, Hao; Yang, Xiaoqi
作者单位：Shenzhen University; ShanghaiTech University; Hong Kong Polytechnic University
摘要：The & ell;1-2 regularization method has a strong sparsity-promoting capability in approaching sparse solutions of linear inverse problems and gains successful applications in various mathematics disciplines and applied science fields. This paper aims to investigate the consistency theory and global convergent algorithms for the & ell;1-2 regularization problem. In the theoretical aspect, we introduce a notion of restricted eigenvalue condition relative to the & ell;1-2 penalty and employ it to...
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作者：Xiao, Nachuan; Ding, Kuangyu; Hu, Xiaoyin; Toh, Kim-Chuan
作者单位：The Chinese University of Hong Kong, Shenzhen; Purdue University System; Purdue University; Shenzhen University; National University of Singapore; National University of Singapore
摘要：In this paper, we consider the minimization of a nonsmooth nonconvex objective function f (x) over a closed convex subset X of Rn, with additional nonsmooth nonconvex constraints c(x) = 0. We develop a unified framework for developing Lagrangian-based methods, which takes a single-step update to the primal variables by some subgradient methods in each iteration. These subgradient methods are embedded into our framework in the sense that they are incorporated as black-box updates to the primal ...
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作者：Bovo, Andrea; De Angelis, Tiziano
作者单位：University of Brescia; University of Turin; Collegio Carlo Alberto
摘要：We prove the existence of a value for two-player zero-sum stopper versus singular-controller games on a finite-time horizon when the underlying dynamics are one-dimensional, diffusive and bound to evolve in [0, infinity). We show that the value is the maximal solution of a variational inequality with both obstacle and gradient constraint and satisfying a Dirichlet boundary condition at [0, T) x {0}. Moreover, we obtain an optimal strategy for the stopper. In order to achieve our goals, we rely...
