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As a wide class of resource management problems in wireless communications are nonconvex and even NP-hard in many cases, finding globally optimal solutions to these problems is of little practical interest. Towards more pragmatic…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where each of the functions $f(x)$ and $g(y)$ is either affine…
We consider nonconvex-concave minimax optimization problems of the form $\min_{\bf x}\max_{\bf y\in{\mathcal Y}} f({\bf x},{\bf y})$, where $f$ is strongly-concave in $\bf y$ but possibly nonconvex in $\bf x$ and ${\mathcal Y}$ is a convex…
In this paper, we use numerical optimization algorithms and a multiscale approach in order to find an optimal well management strategy over the life of the reservoir. The large number of well rates for each control step make the…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
Evolution strategies (ES), as a family of black-box optimization algorithms, recently emerge as a scalable alternative to reinforcement learning (RL) approaches such as Q-learning or policy gradient, and are much faster when many central…
The majorization-minimization (MM) principle is an extremely general framework for deriving optimization algorithms. It includes the expectation-maximization (EM) algorithm, proximal gradient algorithm, concave-convex procedure, quadratic…
Many important machine learning applications amount to solving minimax optimization problems, and in many cases there is no access to the gradient information, but only the function values. In this paper, we focus on such a gradient-free…
Black-box (BB) optimization problems aim to identify an input that maximizes or minimizes the output of a function (the BB function) whose input-output relationship is unknown. Factorization machine with quadratic-optimization annealing…
Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a…
Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising…
We consider stochastic optimization problems with non-convex functional constraints, such as those arising in trajectory generation, sparse approximation, and robust classification. To this end, we put forth a recursive momentum-based…
Let $F$ be a finite model of cardinality $M$ and denote by $\operatorname {conv}(F)$ its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over $\operatorname…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
The success of gradient descent in ML and especially for learning neural networks is remarkable and robust. In the context of how the brain learns, one aspect of gradient descent that appears biologically difficult to realize (if not…
In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization in [BS18a] to quantify the information theoretic…
Cascade ranking is widely used for large-scale top-k selection problems in online advertising and recommendation systems, and learning-to-rank is an important way to optimize the models in cascade ranking. Previous works on learning-to-rank…
We study a variant of a recently introduced min-max optimization framework where the max-player is constrained to update its parameters in a greedy manner until it reaches a first-order stationary point. Our equilibrium definition for this…