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作者：Wirth, Elias; Pena, Javier; Pokutta, Sebastian
作者单位：Technical University of Berlin; Carnegie Mellon University
摘要：Recent papers have shown that the Frank-Wolfe algorithm (FW) with open-loop step-sizes exhibits rates of convergence faster than the iconic O(t-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(t<^>{-1})$$\end{document} rate. In particular, when the minimizer of a strongly convex function over a polyto...
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作者：Gan, Jiarui; Han, Minbiao; Wu, Jibang; Xu, Haifeng
作者单位：University of Oxford; University of Chicago
摘要：This paper provides a systematic study of the robust Stackelberg equilibrium (RSE), which naturally extends the widely adopted solution concept of the strong Stackelberg equilibrium (SSE). The RSE accounts for any possible up-to-delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document} suboptimal...
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作者：Garber, Dan; Kaplan, Atara
作者单位：Technion Israel Institute of Technology
摘要：Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in developing efficient methods for smooth problems that avoid computing expensive high-rank SVDs, advances for nonsmooth problems have been slow paced.In this paper we consider a standard convex relaxation: minimizing a convex nonsmooth objective function over the spectrahedron (set of real positive-semidefinite matrices with unit trac...
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作者：Belotti, Pietro
作者单位：Polytechnic University of Milan
摘要：We consider an n-variate monomial function that is restricted both in value by lower and upper bounds and in domain by two homogeneous linear inequalities. Monomial functions are building blocks for the class of Mixed Integer Nonlinear Optimization problems, which has many practical applications. We show that the upper envelope of the function in the given domain, for n >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepa...
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作者：Brown, Adam; Laddha, Aditi; Pittu, Madhusudhan; Singh, Mohit
作者单位：University System of Georgia; Georgia Institute of Technology; Yale University; Carnegie Mellon University
摘要：In an instance of the weighted Nash Social Welfare problem, we are given a set of m indivisible items, G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}$$\end{document}, and n agents, A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \use...
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作者：Liu, Jia; Chen, Zhiping; Xu, Huifu
作者单位：Xi'an Jiaotong University; Chinese University of Hong Kong
摘要：In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical path and the information on the true utility function is incomplete. To mitigate the adverse impact arising from ambiguity regarding the true utility, we propose a maximin robust model where the optimal policy is based on the worst-case sequence of utility functions from an ambiguity set constructed with partially available information ab...
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作者：Kang, Sumin; Bansal, Manish
作者单位：Virginia Polytechnic Institute & State University
摘要：In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations of DRR- and DRO-MSIPs by presenting multi...
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作者：Wirth, Elias; Pena, Javier; Pokutta, Sebastian
作者单位：Technical University of Berlin; Carnegie Mellon University
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作者：Vaisbourd, Yakov; Choksi, Rustum; Goodwin, Ariel; Hoheisel, Tim; Schonlieb, Carola-Bibiane
作者单位：McGill University; University of Cambridge
摘要：We explore a method of statistical estimation called Maximum Entropy on the Mean (MEM) which is based on an information-driven criterion that quantifies the compliance of a given point with a reference prior probability measure. At the core of this approach lies the MEM function which is a partial minimization of the Kullback-Leibler divergence over a linear constraint. In many cases, it is known that this function admits a simpler representation (known as the Cram & eacute;r rate function). V...
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作者：Xie, Zhonglin; Yin, Wotao; Wen, Zaiwen
作者单位：Peking University; Peking University; Peking University
摘要：Recent years have seen a growing interest in understanding acceleration methods through the lens of ordinary differential equations (ODEs). Despite the theoretical advancements, translating the rapid convergence observed in continuous-time models to discrete-time iterative methods poses significant challenges. In this paper, we present a comprehensive framework integrating the inertial systems with Hessian-driven damping (ISHD) and learning-based approaches for developing optimization methods ...
