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作者：Jin, Xinghu; Pang, Guodong; Xu, Lihu; Xu, Xin
作者单位：Hefei University of Technology; University of Macau; Rice University; South China Normal University
摘要：In this paper, we develop a stochastic algorithm based on the Euler-Maruyama scheme to approximate the invariant measure of the limiting multidimensional diffusion of G/Ph/n + GI queues in the Halfin-Whitt regime. Specifically, we prove a nonasymptotic error bound between the invariant measures of the approximate model from the algorithm and the limiting diffusion. To establish the error bound, we employ the recently developed Stein's method for multidimensional diffusions, in which the regula...
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作者：Del Pia, Alberto; Khajavirad, Aida
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; Lehigh University
摘要：We consider the NP-hard problem of finding the closest rank-one binary tensor to a given binary tensor, which we refer to as the rank-one Boolean tensor factorization (BTF) problem. This optimization problem can be used to recover a planted rankone tensor from noisy observations. We formulate rank-one BTF as the problem of minimizing a linear function over a highly structured multilinear set. Leveraging on our prior results regarding the facial structure of multilinear polytopes, we propose no...
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作者：Lei, Jinlong; Shanbhag, Uday V.
作者单位：Tongji University; Tongji University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample -size stochastic first -order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy -ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates...
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作者：Lambers, Roel; Pendavingh, Rudi; Spieksma, Frits
作者单位：Eindhoven University of Technology
摘要：We investigate a new tournament format that consists of a series of individual knockout tournaments; we call this new format a serial knockout competition (SKC). This format has recently been adopted by the Professional Darts Corporation. Depending on the seedings of the players used for each of the knockout tournaments, players can meet in the various rounds (e.g., first round, second round ... semifinal, final) of the knockout tournaments. Following a fairness principle of treating all playe...
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作者：Possamai, Dylan; Touzi, Nizar
作者单位：New York University; New York University Tandon School of Engineering
摘要：This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov in the extended context allowing for possibly different discount rates for both parties. The agent's problem is to seek for optimal effort given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent's response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump-sum payment at retirem...
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作者：Lu, Shu
摘要：In this paper, we first show how to obtain easy -to -compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution (assuming that the center belongs to a known affine set parallel to the common lineality space of all cones defining the piecewise normal distribution) by using certain skewed projectors on that space. We then extend this method to an asymptotic setting. Next, we apply this method to compute confidence intervals for the true s...
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作者：Fikioris, Giannis; Tardos, Eva
作者单位：Cornell University
摘要：We study the liquid welfare in sequential first-price auctions with budgeted buyers. We use a behavioral model for the buyers, assuming a learning style guarantee: the utility of each buyer is within a gamma factor (gamma >_ 1) of the utility achievable by shading their value with the same factor at each iteration. We show a gamma + 1/2 + O(1/gamma) price of anarchy for liquid welfare when valuations are additive. This is in stark contrast to sequential second-price auctions, where the resulti...
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作者：Ahmadi, Amir Ali; Guenluek, Oktay
作者单位：Princeton University; Cornell University
摘要：A robust-to-dynamics optimization (RDO) problem is an optimization problem spe- cified by two pieces of input: (i) a mathematical program (an objective function f: R -> R and a feasible set QCR) and (it) a dynamical system (a map g: R->). Its goal is to minimize f over the set SCQ of initial conditions that forever remain in Q under g. The focus of this paper is on the case where the mathematical program is a linear program and where the dynamical system is either a known linear map or an unce...
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作者：Ramachandran, Akshay; Shu, Kevin; Wang, Alex L.
作者单位：University System of Georgia; Georgia Institute of Technology; Purdue University System; Purdue University
摘要：This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices SO(n). Such problems are non-convex because of the constraint X E SO(n). Nonetheless, we show that certain linear images of SO(n) are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. Our main technical contributions show that any two-dimensional image of SO(n) is convex and that the projection of SO(...
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作者：Guan, Guohui; Liang, Zongxia; Xia, Jianming
作者单位：Renmin University of China; Renmin University of China; Tsinghua University; Chinese Academy of Sciences
摘要：This paper investigates the equilibrium portfolio selection for smooth ambiguity preferences in a continuous -time market. The investor is uncertain about the risky asset's drift term and updates the subjective belief according to the Bayesian rule. A verification theorem is established, and an equilibrium strategy can be decomposed into a myopic demand and two hedging demands. When the prior is Gaussian, we provide an equilibrium solution in closed form. Moreover, a puzzle in the numerical re...
