Related papers: First Order Stochastic Optimization with Oblivious…

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…

We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs…

We study stochastic zeroth-order (ZO) optimization of smooth nonconvex objectives under heavy-tailed sample-gradient noise. This regime is motivated by empirical evidence that gradient noise in modern machine learning can violate the…

This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased…

This paper delves into stochastic optimization problems that involve Markovian noise. We present a unified approach for the theoretical analysis of first-order gradient methods for stochastic optimization and variational inequalities. Our…

We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…

We consider stochastic optimization problems with heavy-tailed noise with structured density. For such problems, we show that it is possible to get faster rates of convergence than $\mathcal{O}(K^{-2(\alpha - 1)/\alpha})$, when the…

We propose a projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization, where the objective function is a nested composition of $T$ functions and the constraint set is a closed convex…

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…

Two classes of methods have been proposed for escaping from saddle points with one using the second-order information carried by the Hessian and the other adding the noise into the first-order information. The existing analysis for…

This paper is devoted to the study of the solution of a stochastic convex black box optimization problem. Where the black box problem means that the gradient-free oracle only returns the value of objective function, not its gradient. We…

In this work, we consider bilevel optimization when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product (HVP) oracle, one can provably find an $\epsilon$-stationary point within…

Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…

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…

We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…

Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

In this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via…

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…

We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error that can be controlled through a batch size parameter. Our proposed oracles are appealing in several practical contexts, for…