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In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the…

In this paper, we study the problem of finding the global minima of a given function. Specifically, we consider complicated functions with numerous local minima, as is often the case for real-world data mining losses. We do so by applying a…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…

We theoretically study the landscape of the training error for neural networks in overparameterized cases. We consider three basic methods for embedding a network into a wider one with more hidden units, and discuss whether a minimum point…

We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…

The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…

Despite the rich existing literature about minimax optimization in continuous settings, only very partial results of this kind have been obtained for combinatorial settings. In this paper, we fill this gap by providing a characterization of…

A merit (gap) function is a map that returns zero at the solutions of problems and strictly positive values otherwise. Its minimization is equivalent to the original problem by definition, and it can estimate the distance between a given…

We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or…

Predict-then-Optimize is a framework for using machine learning to perform decision-making under uncertainty. The central research question it asks is, "How can the structure of a decision-making task be used to tailor ML models for that…

A long line of works characterizes the sample complexity of regret minimization in sequential decision-making by min-max programs. In the corresponding saddle-point game, the min-player optimizes the sampling distribution against an…

We present two algorithms for large-scale low-rank Euclidean distance matrix completion problems, based on semidefinite optimization. Our first method works by relating cliques in the graph of the known distances to faces of the positive…

Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…

In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output…

Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…

In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…

A tenet of reinforcement learning is that the agent always observes rewards. However, this is not true in many realistic settings, e.g., a human observer may not always be available to provide rewards, sensors may be limited or…

In real-world applications, users often favor structurally diverse design choices over one high-quality solution. It is hence important to consider more solutions that decision makers can compare and further explore based on additional…

Markov decision processes (MDPs) are widely used in modeling decision making problems in stochastic environments. However, precise specification of the reward functions in MDPs is often very difficult. Recent approaches have focused on…