2期

最新文章

• Convexification of Bilinear Terms over Network Polytopes AI翻译
  作者：Khademnia, Erfan; Davarnia, Danial
  作者单位：Iowa State University
  摘要：It is well-known that the McCormick relaxation for the bilinear constraint z = xy gives the convex hull over the box domains for x and y . In network applications where the domain of bilinear variables is described by a network polytope, the McCormick relaxation, also referred to as linearization, fails to provide the convex hull and often leads to poor dual bounds. We study the convex hull of the set containing bilinear constraints z i , j = xiyj i y j where xi i represents the arc -flow vari...
• Corruption-Robust Exploration in Episodic Reinforcement Learning AI翻译
  作者：Lykouris, Thodoris; Simchowitz, Max; Slivkins, Aleksandrs; Sun, Wen
  作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Cornell University
  摘要：We initiate the study of episodic reinforcement learning (RL) under adversarial corruptions in both the rewards and the transition probabilities of the underlying system, extending recent results for the special case of multiarmed bandits. We provide a framework that modifies the aggressive exploration enjoyed by existing reinforcement learning approaches based on optimism in the face of uncertainty by complementing them with principles from action elimination. Importantly, our framework circu...
• Optimal Error Bounds in the Absence of Constraint Qualifications with Applications to p-Cones and Beyond AI翻译
  作者：Lindstrom, Scott B.; Lourenco, Bruno F.; Pong, Ting Kei
  作者单位：Curtin University; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; Hong Kong Polytechnic University
  摘要：We prove tight Holderian lderian error bounds for all p -cones. Surprisingly, the exponents differ in several ways from those that have been previously conjectured. Moreover, they illuminate p -cones as a curious example of a class of objects that possess properties in three dimensions that they do not in four or more. Using our error bounds, we analyse least squares problems with p -norm regularization, where our results enable us to compute the corresponding Kurdyka-& Lstrok;ojasiewicz expon...
• Learning and Balancing Unknown Loads in Large-Scale Systems AI翻译
  作者：Goldsztajn, Diego; Borst, Sem C.; van Leeuwaarden, Johan S. H.
  作者单位：Eindhoven University of Technology; Inria; Tilburg University
  摘要：Consider a system of identical server pools where tasks with exponentially distributed service times arrive as a time-inhomogeneous Poisson process. An admission threshold is used in an inner control loop to assign incoming tasks to server pools, while in an outer control loop, a learning scheme adjusts this threshold over time to keep it aligned with the unknown offered load of the system. In a many-server regime, we prove that the learning scheme reaches an equilibrium along intervals of tim...
• Investment Timing and Technological Breakthroughs AI翻译
  作者：Decamps, Jean-Paul; Gensbittel, Fabien; Mariotti, Thomas
  作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse 1 Capitole; Centre for Economic Policy Research - UK; Leibniz Association; Ifo Institut
  摘要：We study the optimal investment policy of a firm facing both technological and cash-flow uncertainty. At any point in time, the firm can irreversibly invest in a standalone technology or wait for a technological breakthrough. Breakthroughs occur when market conditions become favorable enough, exceeding a threshold value that is ex ante unknown to the firm. The Markov state variables for the optimal investment policy are the current market conditions and their historic maximum, and the firm opt...
• Robust Multiple Stopping-A Duality Approach AI翻译
  作者：Laeven, Roger J. A.; Schoenmakers, John G. M.; Schweizer, Nikolaus; Stadje, Mitja
  作者单位：University of Amsterdam; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Tilburg University; Ulm University; Ulm University
  摘要：We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights-that is, optimal multiple stopping-for a robust evaluation that accounts for model uncertainty with a dominated family of priors and for general reward processes driven by multidimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem that satisfy appea...
• Markov Decision Processes with Observation Costs: Framework and Computation with a Penalty Scheme AI翻译
  作者：Reisinger, Christoph; Tam, Jonathan
  作者单位：University of Oxford
  摘要：We consider Markov decision processes where the state of the chain is only given at chosen observation times and of a cost. Optimal strategies involve the optimization of observation times as well as the subsequent action values. We consider the finite horizon and discounted infinite horizon problems as well as an extension with parameter uncertainty. By including the time elapsed from observations as part of the augmented Markov system, the value function satisfies a system of quasivariationa...
• Estimating a Function and Its Derivatives Under a Smoothness Condition AI翻译
  作者：Lim, Eunji
  作者单位：Adelphi University
  摘要：We consider the problem of estimating an unknown function f & lowast; : Rd d -> R and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f & lowast; except that it is smooth in the sense that it has square integrable partial derivatives of order m . A natural candidate for the estimator of f & lowast; in such a case is the best fit to the data set that satisfies a certain smoothness condition. This estimator can be seen as a least squares estima...
• r-Arbitrage and r-Consistent Pricing for Star-Shaped Risk Measures AI翻译
  作者：Herdegen, Martin; Khan, Nazem
  作者单位：University of Warwick; Dublin City University
  摘要：This paper revisits mean-risk portfolio selection in a one-period financial market, where risk is quantified by a star-shaped risk measure rho. We make three contributions. First, we introduce the new axiom of sensitivity to large expected losses and show that it is key to ensure the existence of optimal portfolios. Second, we give primal and dual characterizations of (strong) rho-arbitrage. Finally, we use our conditions for the absence of (strong) rho-arbitrage to explicitly derive the (stro...
• On the Simplex Method for 0/1-Polytopes AI翻译
  作者：Black, Alexander E.; De Loera, Jestis A.; Kafer, Sean; Sanita, Laura
  作者单位：University of California System; University of California Davis; University System of Georgia; Georgia Institute of Technology; Bocconi University
  摘要：We present three new pivot rules for the Simplex method for Linear Programs over 0/1-polytopes. We show that the number of nondegenerate steps taken using these three rules is strongly polynomial, linear in the number of variables, and linear in the dimension. Our bounds on the number of steps are asymptotically optimal on several well-known combinatorial polytopes. Our analysis is based on the geometry of 0/1 -polytopes and novel modifications to the classical steepest -edge and shadow -verte...