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作者：Luo, Yiyun; Sun, Will Wei; Liu, Yufeng
作者单位：Shanghai University of Finance & Economics; Purdue University System; Purdue University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customer's valuation for the product is a linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customer's true valuation, but instead needs to learn the valuation by leveraging contextual information and histo...
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作者：Correa, Jose; Cristi, Andres; Epstein, Boris; Soto, Jose A.
作者单位：Universidad de Chile; Universidad de Chile; Columbia University
摘要：We take a unifying approach to single selection optimal stopping problems with random arrival order and independent sampling of items. In the problem we consider, a decision maker (DM) initially gets to sample each of N items independently with probability p, and can observe the relative rankings of these sampled items. Then, the DM faces the remaining items in an online fashion, observing the relative rankings of all revealed items. While scanning the sequence the DM makes irrevocable stop/co...
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作者：Hoai An Le Thi; Van Ngai Huynh; Tao Pham Dinh
作者单位：Universite de Lorraine; Institut Universitaire de France
摘要：We address the so-called DC (difference -of -convex functions) composite minimization problems (or DC composite programs ) whose objective function is a composition of a DC function with a continuously differentiable mapping. We first develop an algorithm named DC composite algorithm (DCCA in short) for unconstrained DC composite programs and further extend to DC composite programs with constraints of inclusion associated with a smooth mapping and a closed convex set. The convergence analysis ...
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作者：Hayashi, Koyo; Hirai, Hiroshi; Sakabe, Keiya
作者单位：University of Tokyo; Nagoya University; University of Tokyo
摘要：Given a nonnegative matrix A=(A(ij))=, the matrix scaling problem asks whether A can be scaled to a doubly stochastic matrix D1AD2 for some positive diagonal matrices D-1, D-2. The Sinkhorn algorithm is a simple iterative algorithm, which repeats row-normalization A(ij )<- A(ij)/& sum;(i)A(ij) and column-normalization A(ij )<- A(ij)/& sum;(i)A(ij) alternatively. By this algorithm, A converges to a doubly stochastic matrix in limit if and only if the bipartite graph associated with A has a perf...
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作者：Birgin, Ernesto G.; Gardenghi, John L.; Laurain, Antoine
作者单位：Universidade de Sao Paulo; Universidade de Brasilia; University of Duisburg Essen
摘要：The problem of covering a two-dimensional bounded set with a fixed number of minimum-radius identical disks is studied in the present work. Bounds on the optimal radius are obtained for a certain class of nonsmooth domains, and an asymptotic expansion of the bounds as the number of disks goes to infinity is provided. The proof is based on the approximation of the set to be covered by hexagonal honeycombs and on the thinnest covering property of the regular hexagonal lattice arrangement in the ...
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作者：Xiao, Nachuan; Liu, Xin; Toh, Kim-Chuan
作者单位：National University of Singapore; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; National University of Singapore
摘要：In this paper, we consider optimization problems over closed embedded submanifolds of Rn, which are defined by the constraints c(x) = 0. We propose a class of constraint-dissolving approaches for these Riemannian optimization problems. In these proposed approaches, solving a Riemannian optimization problem is transferred into the unconstrained minimization of a constraint-dissolving function (CDF). Different from existing exact penalty functions, the exact gradient and Hessian of CDF are easy ...
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作者：Guo, Xin; Huang, Yonghui; Zhang, Yi
作者单位：Sun Yat Sen University; Sun Yat Sen University; University of Birmingham
摘要：This paper studies Borel models of nonstationary Markov decision processes (MDPs) with average criteria. We establish a suitable fixed point theorem, which is used to show the existence of solutions to the average optimality equation (AOE), without using contractions. The existence of optimal policies follows from the obtained solutions to the AOE. Furthermore, we show that versions of the rolling horizon algorithm can be used to produce an optimal policy or an epsilon-optimal policy. Finally,...
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作者：Glover, Kristoffer; Peskir, Goran
作者单位：University of Technology Sydney; University of Manchester
摘要：Consider an Ornstein-Uhlenbeck process that initially reverts to zero at a known mean-reversion rate beta 0, and then after some random/unobservable time, this meanreversion rate is changed to beta 1. Assuming that the process is observed in real time, the problem is to detect when exactly this change occurs as accurately as possible. We solve this problem in the most uncertain scenario when the random/unobservable time is (i) exponentially distributed and (ii) independent from the process pri...
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作者：Liang, Jiaming; Monteiro, Renato D. C.
作者单位：Yale University; University System of Georgia; Georgia Institute of Technology
摘要：This paper presents a proximal bundle (PB) framework based on a generic bun-dle update scheme for solving the hybrid convex composite optimization (HCCO) problem and establishes a common iteration-complexity bound for any variant belonging to it. As a consequence, iteration-complexity bounds for three PB variants based on different bundle update schemes are obtained in the HCCO context for the first time and in a unified man-ner. Although two of the PB variants are universal (i.e., their imple...
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作者：Nishimura, Hiroki; Ok, Efe A.
作者单位：University of California System; University of California Riverside; New York University; New York University
摘要：We propose a class of semimetrics for acyclic preference relations, any one of which is an alternative to the classical Kemeny-Snell-Bogart metric. These semimetrics are based solely on the implications of preferences for choice behavior and thus appear more suitable in economic contexts and choice experiments. We obtain a fairly simple axiomatic characterization for the class we propose. The apparently most important member of this class, which we dub the top-difference semimetric, is charact...
