Related papers: Fully Zeroth-Order Bilevel Programming via Gaussia…
Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, specially when the objective is to improve the performance of a stochastic system. However, the performance of these…
Optimization problems with access to only zeroth-order information of the objective function on Riemannian manifolds arise in various applications, spanning from statistical learning to robot learning. While various zeroth-order algorithms…
In this work, we focus on the study of stochastic zeroth-order (ZO) optimization which does not require first-order gradient information and uses only function evaluations. The problem of ZO optimization has emerged in many recent machine…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
In this paper, we introduce a powerful and efficient framework for direct optimization of ranking metrics. The problem is ill-posed due to the discrete structure of the loss, and to deal with that, we introduce two important techniques:…
Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration…
The problem of recovering partial derivatives of high orders of bivariate functions with finite smoothness is studied. Based on the truncation method, a numerical differentiation algorithm was constructed, which is optimal by the order,…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multilevel Monte Carlo method recently introduced by Giles (Giles 2008) to the framework of stochastic optimization by means of…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained…
We propose an enhanced zeroth-order stochastic Frank-Wolfe framework to address constrained finite-sum optimization problems, a structure prevalent in large-scale machine-learning applications. Our method introduces a novel double variance…
In this paper, we propose the Bi-Sub-Gradient (Bi-SG) method, which is a generalization of the classical sub-gradient method to the setting of convex bi-level optimization problems. This is a first-order method that is very easy to…
Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the…
Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning applications. It is used for solving optimization problems similarly to gradient-based methods. However, it…
In this article, we propose and develop a novel Bayesian algorithm for optimization of functions whose first and second partial derivatives are known. The basic premise is the Gaussian process representation of the function which induces a…
In this paper, we introduce an unbiased gradient simulation algorithms for solving convex optimization problem with stochastic function compositions. We show that the unbiased gradient generated from the algorithm has finite variance and…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
In this paper, we focus on solving an important class of nonconvex optimization problems which includes many problems for example signal processing over a networked multi-agent system and distributed learning over networks. Motivated by…