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Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…

Machine Learning · Computer Science 2019-05-07 Andrew An Bian , Baharan Mirzasoleiman , Joachim M. Buhmann , Andreas Krause

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization (QDSFM), which allows to model a number of learning tasks on graphs and hypergraphs. The problem exhibits close ties to…

Machine Learning · Computer Science 2020-10-27 Pan Li , Niao He , Olgica Milenkovic

The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…

Data Structures and Algorithms · Computer Science 2017-12-01 Simon Bruggmann , Rico Zenklusen

We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as…

Optimization and Control · Mathematics 2023-07-20 Timo Kreimeier , Sebastian Pokutta , Andrea Walther , Zev Woodstock

We study a class of convex-concave saddle-point problems of the form $\min_x\max_y \langle Kx,y\rangle+f_{\cal{P}}(x)-h^\ast(y)$ where $K$ is a linear operator, $f_{\cal{P}}$ is the sum of a convex function $f$ with a Lipschitz-continuous…

Optimization and Control · Mathematics 2021-06-07 Vladimir Kolmogorov , Thomas Pock

Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient…

Machine Learning · Statistics 2018-06-15 Lin Chen , Christopher Harshaw , Hamed Hassani , Amin Karbasi

We consider the problem of minimizing the sum of two convex functions. One of those functions has Lipschitz-continuous gradients, and can be accessed via stochastic oracles, whereas the other is "simple". We provide a Bregman-type algorithm…

Optimization and Control · Mathematics 2024-11-26 Benjamin Dubois-Taine , Francis Bach , Quentin Berthet , Adrien Taylor

In this paper, we consider the optimization problem \scpl (\scp), which is to find a minimum cost subset of a ground set $U$ such that the value of a submodular function $f$ is above a threshold $\tau$. In contrast to most existing work on…

Data Structures and Algorithms · Computer Science 2022-11-10 Victoria G. Crawford

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…

Data Structures and Algorithms · Computer Science 2016-04-19 Moran Feldman

The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational…

Optimization and Control · Mathematics 2021-06-15 Cyrille W. Combettes , Sebastian Pokutta

Performative reinforcement learning is an emerging dynamical decision making framework, which extends reinforcement learning to the common applications where the agent's policy can change the environmental dynamics. Existing works on…

Machine Learning · Computer Science 2025-10-07 Ziyi Chen , Heng Huang

Recently the away-step Frank-Wolfe algoritm for constrained multiobjective optimization has been shown linear convergence rate over a polytope which is generated by finite points set. In this paper we design a decomposition-invariant…

Optimization and Control · Mathematics 2024-09-10 Zhuoxin Fan , Liping Tang

The problem of monotone submodular maximization has been studied extensively due to its wide range of applications. However, there are cases where one can only access the objective function in a distorted or noisy form because of the…

Data Structures and Algorithms · Computer Science 2022-10-24 Lingxiao Huang , Yuyi Wang , Chunxue Yang , Huanjian Zhou

In this paper, we develop an $O((m \log k) {\rm MSF} (n,m,1))$-time algorithm to find a half-integral node-capacitated multiflow of the maximum total flow-value in a network with $n$ nodes, $m$ edges, and $k$ terminals, where ${\rm MSF}…

Data Structures and Algorithms · Computer Science 2018-10-30 Hiroshi Hirai

Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been…

Computer Vision and Pattern Recognition · Computer Science 2015-10-27 Hector Allende , Emanuele Frandi , Ricardo Nanculef , Claudio Sartori

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or…

Optimization and Control · Mathematics 2017-11-01 Vasileios Tzoumas , Konstantinos Gatsis , Ali Jadbabaie , George J. Pappas

We consider two greedy algorithms for minimizing a convex function in a bounded convex set: an algorithm by Jones [1992] and the Frank-Wolfe (FW) algorithm. We first consider approximate versions of these algorithms. For smooth convex…

Optimization and Control · Mathematics 2018-11-19 Nan Ye , Peter Bartlett

We propose an enhanced zeroth-order stochastic Frank-Wolfe framework to address constrained finite-sum optimization problems, a structure prevalent in large-scale machine-learning applications. Our method introduces a novel double variance…

Machine Learning · Computer Science 2025-01-24 Haishan Ye , Yinghui Huang , Hao Di , Xiangyu Chang

In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first…

Optimization and Control · Mathematics 2022-06-20 Baojian Zhou , Yifan Sun

In monotone submodular function maximization, approximation guarantees based on the curvature of the objective function have been extensively studied in the literature. However, the notion of curvature is often pessimistic, and we rarely…

Data Structures and Algorithms · Computer Science 2017-09-12 Tasuku Soma , Yuichi Yoshida