Mathematics of Operations Research

最新文章

• Lipschitz Bernoulli Utility Functions AI翻译
  作者：Ok, Efe A.; Weaver, Nik
  作者单位：New York University; New York University; Washington University (WUSTL)
  摘要：We obtain several variants of the classic von Neumann-Morgenstern expected utility theorem with and without the completeness axiom in which the derived Bernoulli utility functions are Lipschitz. The prize space in these results is an arbitrary separable metric space, and the utility functions are allowed to be unbounded. The main ingredient of our results is a novel (behavioral) axiom on the underlying preference relations, which is satisfied by virtually all stochastic orders. The proof of th...
• On Singular Control for Levy Processes AI翻译
  作者：Noba, Kei; Yamazaki, Kazutoshi
  作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; University of Queensland
  摘要：We revisit the classical singular control problem of minimizing running and controlling costs. Existing studies have shown the optimality of a barrier strategy when driven by Brownian motion or Levy processes with one-sided jumps. Under the assumption that the running cost function is convex, we show the optimality of a barrier strategy for a general class of Levy processes.
• Asymptotically Optimal Control of Make-to-Stock Systems AI翻译
  作者：Gao, Xuefeng; Huang, Junfei
  作者单位：Chinese University of Hong Kong; Chinese University of Hong Kong
  摘要：We consider multiclass make-to-stock production/inventory systems in which the manager makes three decisions, including pricing, outsourcing, and scheduling, to maximize the long-run average profit. For a sequence of systems in the heavy-traffic regime, with linear or strictly convex holding/waiting cost functions, we propose a sequence of policies and establish its asymptotic optimality. Our proof combines the lower bound approach and a thorough steady-state analysis of the systems. We also e...
• Combinatorial Auctions with Interdependent Valuations: SOS to the Rescue AI翻译
  作者：Eden, Alon; Feldman, Michal; Fiat, Amos; Goldner, Kira; Karlin, Anna R.
  作者单位：Hebrew University of Jerusalem; Tel Aviv University; Boston University; University of Washington; University of Washington Seattle
  摘要：We study combinatorial auctions with interdependent valuations, where each agent i has a private signal si that captures her private information and the valuation function of every agent depends on the entire signal profile, s = (s1,...,sn). The literature in economics shows that the interdependent model gives rise to strong impossibility results and identifies assumptions under which optimal solutions can be attained. The computer science literature provides approximation results for simple s...
• Stationary Discounted and Ergodic Mean Field Games with Singular Controls AI翻译
  作者：Cao, Haoyang; Dianetti, Jodi; Ferrari, Giorgio
  作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; University of Bielefeld
  摘要：We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and ergodic performance criteria. This class of games finds natural applications in the context of optimal productivity expansion in dynamic oligopolies. We prove the existence and uniqueness of the mean field equilibria, which are completely characterized through nonlinear equations. Furthermore, we relate the mean fi...
• A Sensitivity Analysis of the Price of Anarchy in Nonatomic Congestion Games AI翻译
  作者：Wu, Zijun; Moehring, Rolf H.
  作者单位：Hefei University; Technical University of Berlin
  摘要：The price of anarchy (PoA) is a standard measure to quantify the inefficiency of equilibria in nonatomic congestion games. Most publications have focused on worst-case bounds for the PoA. Only a few have analyzed the sensitivity of the PoA against changes of the demands or cost functions, although that is crucial for empirical computations of the PoA. We analyze the sensitivity of the PoA with respect to (w.r.t.) simultaneous changes of demands and cost functions. The key to this analysis is a...
• Provably Efficient Reinforcement Learning with Linear Function Approximation AI翻译
  作者：Jin, Chi; Yang, Zhuoran; Wang, Zhaoran; Jordan, Michael, I
  作者单位：Princeton University; Yale University; Northwestern University; University of California System; University of California Berkeley
  摘要：Modern reinforcement learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of function approximation raises a fundamental set of challenges involving computational and statistical efficiency, especially given the need to manage the exploration/exploitation trade-off. As a result, a core RL question remains open: how can we design provably e...
• Exact Optimal Stopping for Multidimensional Linear Switching Diffusions AI翻译
  作者：Ernst, Philip; Mei, Hongwei
  作者单位：Rice University; Imperial College London; Texas Tech University System; Texas Tech University
  摘要：The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: The underlying stochastic process has discontinuous paths, and the cost function is not necessarily integrable on the entire time horizon, where the latter is often a key assumption in classical optimal stopping theory for diffusions. Under relatively mild conditions, we show, for the class of multidimens...
• A General Framework for Bandit Problems Beyond Cumulative Objectives AI翻译
  作者：Cassel, Asaf; Mannor, Shie; Zeevi, Assaf
  作者单位：Tel Aviv University; Technion Israel Institute of Technology; Technion Israel Institute of Technology; Columbia University; Columbia University
  摘要：The stochastic multiarmed bandit (MAB) problem is a common model for sequential decision problems. In the standard setup, a decision maker has to choose at every instant between several competing arms; each of them provides a scalar random variable, referred to as a reward. Nearly all research on this topic considers the total cumulative reward as the criterion of interest. This work focuses on other natural objectives that cannot be cast as a sum over rewards but rather, more involved functio...
• On the Efficient Implementation of the Matrix Exponentiated Gradient Algorithm for Low-Rank Matrix Optimization AI翻译
  作者：Garber, Dan; Kaplan, Atara
  作者单位：Technion Israel Institute of Technology
  摘要：Convex optimization over the spectrahedron, that is, the set of all real n x n positive semidefinite matrices with unit trace, has important applications in machine learning, signal processing, and statistics, mainly as a convex relaxation for optimization problems with low-rank matrices. It is also one of the most prominent examples in the theory of first order methods for convex optimization in which non-Euclidean methods can be significantly preferable to their Euclidean counterparts. In pa...