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作者：Chen, Fan; Conforti, Giovanni; Ren, Zhenjie; Wang, Xiaozhen
作者单位：Shanghai Jiao Tong University; University of Padua; Universite PSL; Universite Paris-Dauphine
摘要：In this paper, we study the entropic martingale optimal transport (EMOT) problem on R. The investigation of the EMOT problem arises in the calibration problem of the stochastic volatility models, where martingale constraints reflect no-arbitrage pricing conditions under the risk-neutral measure, as originally proposed by Henry-Laborde`re. We first establish the dual formulation of the EMOT problem and prove that Sinkhorn's algorithm achieves an exponential convergence rate under mild condition...
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作者：Zhang, Xilin; Cheung, Wang Chi
作者单位：National University of Singapore
摘要：We study a general reusable resource allocation model under both model uncertainty and nonstationarity. Our study involves a set of heterogeneous customers who arrive sequentially at the decision maker's (DM's) platform, each associated with a different customer type. Each arriving customer's type is drawn from an unknown and time-varying probability distribution. Upon observing the customer's type, the DM selects an allocation decision that generates a random amount of reward and occupies ran...
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作者：Bayraktar, Erhan; Han, Bingyan
作者单位：University of Michigan System; University of Michigan; Hong Kong University of Science & Technology (Guangzhou)
摘要：Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized optimal transport with general f-divergence. Under the bicausal constraint, we introduce the concept of equilibrium transport. Existence is proved in the semidiscrete Markovian case and the continuous non-Markovian case with strict quasiconvexity, whereas unique...
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作者：Zhong, Xianghui
作者单位：University of Bonn
摘要：One way to speed up the calculation of optimal traveling salesman problem tours in practice is eliminating edges that are certainly not in the optimal tour as a preprocessing step. In order to do so, several edge elimination approaches have been proposed in the past. In this work, we investigate two of them in the scenario where the input consists of n independently distributed random points in the two-dimensional unit square with density function bounded from above and below by arbitrary posi...
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作者：Gao, Xuefeng; Zhou, Xunyu
作者单位：Chinese University of Hong Kong; Columbia University
摘要：We study reinforcement learning for continuous-time Markov decision processes (MDPs) in the finite-horizon episodic setting. In contrast to discrete-time MDPs, the intertransition times of a continuous-time MDP are exponentially distributed with rate parameters depending on the state-action pair at each transition. We present a learning algorithm based on the methods of value iteration and upper confidence bound. We derive an upper bound on the worst case expected regret for the proposed algor...
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作者：Huang, Zhihan; Wei, Yuting; Chen, Yuxin
作者单位：University of Pennsylvania
摘要：The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative artificial intelligence. Although sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional to the ambient data dimension, resulting in overly conservative theory that fails to explain its practical efficiency. This has motivated the recent work to investigate how the DDPM can achieve sampling speed-ups through automatic expl...
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作者：Bei, Xiaohui; Li, Zihao; Luo, Junjie
作者单位：Nanyang Technological University; National University of Singapore; Beijing Jiaotong University
摘要：We study the problem of allocating multiple types of resources to agents with Leontief preferences. The classic Dominant Resource Fairness (DRF) mechanism satisfies several desired fairness and incentive properties, but is known to have poor performance in terms of social welfare approximation ratio. In this work, we propose a new approximation ratio measure, called fair-ratio, which is defined as the worst-case ratio between the optimal social welfare (resp. utilization) among all fair alloca...
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作者：Han, Xiyue; Schied, Alexander
作者单位：University of Waterloo
摘要：We study the problem of reconstructing the Faber-Schauder coefficients of a continuous functionf from discrete observations of its antiderivative F. For instance, this question arises in financial mathematics when estimating the roughness of volatility from the integrated volatility of an asset price trajectory. Our approach starts with mathematically formulating the reconstruction problem through piecewise quadratic spline interpolation. We then provide a closed-form solution and an in-depth ...
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作者：Kurpisz, Adam; Potechin, Aaron; Wirth, Elias
作者单位：ETH Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Chicago; Technical University of Berlin
摘要：We introduce several methods to study the rank of the sum of squares (SoS) hierarchy for problems over the Boolean hypercube. We apply our techniques to improve upon existing results, thus answering several open questions. We answer the question by Laurent regarding the SoS rank of the empty integral hull (EIH) problem. We prove that the SoS rank is between inverted right perpendicularn/2inverted left perpendicular and inverted right perpendicularn/2+ root n log 2ninverted left perpendicular. ...
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作者：Iglesias, Martin Amaiz; Cetingoz, Adil Rengim; Frikha, Noufel
摘要：This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and subadditive risk measures. We employ mirror descent algorithms to determine the optimal risk budgeting weights in both deterministic and stochastic settings, establishing convergence along with an explicit nonasymptotic quantitative rate for the averaged algorithm. A comprehensive numerical analysis follows, illustrating our theoretical findings acro...
