Related papers: A Unified Approach to Minimizing Symmetric Submodu…

Many tasks in machine learning and data mining, such as data diversification, non-parametric learning, kernel machines, clustering etc., require extracting a small but representative summary from a massive dataset. Often, such problems can…

We consider the problem of maximizing the multilinear extension of a submodular function subject a single matroid constraint or multiple packing constraints with a small number of adaptive rounds of evaluation queries. We obtain the first…

Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…

In this work, we consider a connected network of finitely many agents working cooperatively to solve a min-max problem with convex-concave structure. We propose a decentralised first-order algorithm which can be viewed as a non-trivial…

We introduce the Stochastic Monotone Aggregated Root-Finding (SMART) algorithm, a new randomized operator-splitting scheme for finding roots of finite sums of operators. These algorithms are similar to the growing class of incremental…

In this paper, we provide near-optimal accelerated first-order methods for minimizing a broad class of smooth nonconvex functions that are strictly unimodal on all lines through a minimizer. This function class, which we call the class of…

We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization…

This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. Current state-of-the-art first-order algorithms find an…

Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…

We introduce a new class of functions that can be minimized in polynomial time in the value oracle model. These are functions $f$ satisfying $f(x)+f(y)\ge f(x \sqcap y)+f(x \sqcup y)$ where the domain of each variable $x_i$ corresponds to…

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

Recently, flat-minima optimizers, which seek to find parameters in low-loss neighborhoods, have been shown to improve a neural network's generalization performance over stochastic and adaptive gradient-based optimizers. Two methods have…

In the online metric bipartite matching problem, we are given a set $S$ of server locations in a metric space. Requests arrive one at a time, and on its arrival, we need to immediately and irrevocably match it to a server at a cost which is…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…

In this work, we reveal a rich combinatorial structure underlying exact minimax optimal algorithms for classical nonexpansive fixed-point problems. This viewpoint unifies all extremal optimal methods and provides a systematic and practical…

Submodularity is an important property of set functions and has been extensively studied in the literature. It models set functions that exhibit a diminishing returns property, where the marginal value of adding an element to a set…

In the framework of convolutional neural networks, downsampling is often performed with an average-pooling, where all the activations are treated equally, or with a max-pooling operation that only retains an element with maximum activation…

This letter presents an almost sure convergence of the zeroth-order mirror descent algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate…

Sorting is a fundamental operation in computer systems and is widely used in applications such as databases, data analytics, and hardware accelerators. Unary computing has recently emerged as a low-cost and power-efficient paradigm for…

Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…