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Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
This paper considers the distributed online bandit optimization problem with nonconvex loss functions over a time-varying digraph. This problem can be viewed as a repeated game between a group of online players and an adversary. At each…
The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and…
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…
Variance-reduced gradient estimators for policy gradient methods have been one of the main focus of research in the reinforcement learning in recent years as they allow acceleration of the estimation process. We propose a variance-reduced…
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…
An Adagrad-inspired class of algorithms for smooth unconstrained optimization is presented in which the objective function is never evaluated and yet the gradient norms decrease at least as fast as $\calO(1/\sqrt{k+1})$ while second-order…
We develop an online gradient algorithm for optimizing the performance of product-form networks through online adjustment of control parameters. The use of standard algorithms for finding optimal parameter settings is hampered by the…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
An algorithm is proposed for solving optimization problems with stochastic objective and deterministic equality and inequality constraints. This algorithm is objective-function-free in the sense that it only uses the objective's gradient…
We study a high-dimensional regression setting under the assumption of known covariate distribution. We aim at estimating the amount of explained variation in the response by the best linear function of the covariates (the signal level). In…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
A new formulation of Stochastic Model Predictive Output Feedback Control is presented and analyzed as a translation of Stochastic Optimal Output Feedback Control into a receding horizon setting. This requires lifting the design into a…
This paper tackles the problem of solving stochastic optimization problems with a decision-dependent distribution in the setting of stochastic strongly-monotone games and when the distributional dependence is unknown. A two-stage approach…
In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…
We design an algorithm which finds an $\epsilon$-approximate stationary point (with $\|\nabla F(x)\|\le \epsilon$) using $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector products, matching guarantees that were previously available…
Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…
From the perspective of control theory, the gradient descent optimization methods can be regarded as a dynamic system where various control techniques can be designed to enhance the performance of the optimization method. In this paper, we…