Related papers: A note on the Minimum Norm Point algorithm
Machine learning algorithms typically perform optimization over a class of non-convex functions. In this work, we provide bounds on the fundamental hardness of identifying the global minimizer of a non convex function. Specifically, we…
We consider submodular function minimization in the oracle model: given black-box access to a submodular set function $f:2^{[n]}\rightarrow \mathbb{R}$, find an element of $\arg\min_S \{f(S)\}$ using as few queries to $f(\cdot)$ as…
Submodularity is a key property in discrete optimization. Submodularity has been widely used for analyzing the greedy algorithm to give performance bounds and providing insight into the construction of valid inequalities for mixed-integer…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary…
In this work, we propose a novel optimization model termed "sum-of-minimum" optimization. This model seeks to minimize the sum or average of $N$ objective functions over $k$ parameters, where each objective takes the minimum value of a…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Submodular optimization with bandit feedback has recently been studied in a variety of contexts. In a number of real-world applications such as diversified recommender systems and data summarization, the submodular function exhibits…
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…
Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…
In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large…