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A variant of consensus based distributed gradient descent (\textbf{DGD}) is studied for finite sums of smooth but possibly non-convex functions. In particular, the local gradient term in the fixed step-size iteration of each agent is…
This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
Large-scale non-convex optimization problems are expensive to solve due to computational and memory costs. To reduce the costs, first-order (computationally efficient) and asynchronous-parallel (memory efficient) algorithms are necessary to…
In recent years, feature selection has become a challenging problem in several machine learning fields, such as classification problems. Support Vector Machine (SVM) is a well-known technique applied in classification tasks. Various…
Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of…
Efficiently solving multi-objective optimization problems for simulation optimization of important scientific and engineering applications such as materials design is becoming an increasingly important research topic. This is due largely to…
We explore the local landscape of low-rank matrix recovery, focusing on reconstructing a $d_1\times d_2$ matrix $X^\star$ with rank $r$ from $m$ linear measurements, some potentially noisy. When the noise is distributed according to an…
We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current…
Decentralized optimization methods often entail information exchange between neighbors. Transmission failures can happen due to network congestion, hardware/software issues, communication outage, and other factors. In this paper, we…
The difficulty of minimizing a nonconvex function is in part explained by the presence of saddle points. This slows down optimization algorithms and impacts worst-case complexity guarantees. However, many nonconvex problems of interest…
Real-time visual analysis tasks, like tracking and recognition, require swift execution of computationally intensive algorithms. Visual sensor networks can be enabled to perform such tasks by augmenting the sensor network with processing…
Finding lower and better-generalizing minima is crucial for deep learning. However, most existing optimizers stop searching the parameter space once they reach a local minimum. Given the complex geometric properties of the loss landscape,…
We consider stochastic optimization problems in multi-agent settings, where a network of agents aims to learn parameters which are optimal in terms of a global objective, while giving preference to locally observed streaming information. To…
We develop a variational minimax method for detecting maximal saddle-node bifurcations in abstract nonlinear equations. Unlike continuation and path-following techniques, the method identifies the critical parameter directly as an extremal…
We study reward maximisation in a wide class of structured stochastic multi-armed bandit problems, where the mean rewards of arms satisfy some given structural constraints, e.g. linear, unimodal, sparse, etc. Our aim is to develop methods…
Many tasks in modern machine learning can be formulated as finding equilibria in \emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…