Related papers: Zeroth-order Random Subspace Algorithm for Non-smo…
In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…
We investigate the finite-time analysis of finding ($\delta,\epsilon$)-stationary points for nonsmooth nonconvex objectives in decentralized stochastic optimization. A set of agents aim at minimizing a global function using only their local…
Finding the global minimum of non-convex functions is one of the main and most difficult problems in modern optimization. In the first part of the paper, we consider a certain class of "good" non-convex functions that can be bounded above…
Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is…
Many convex optimization problems have structured objective function written as a sum of functions with different types of oracles (full gradient, coordinate derivative, stochastic gradient) and different evaluation complexity of these…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…
This paper considers the problem for finding the $(\delta,\epsilon)$-Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of important applications. We construct a zeroth-order…
We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…
A parametric class of trust-region algorithms for unconstrained nonconvex optimization is considered where the value of the objective function is never computed. The class contains a deterministic version of the first-order Adagrad method…
We give nearly matching upper and lower bounds on the oracle complexity of finding $\epsilon$-stationary points ($\| \nabla F(x) \| \leq\epsilon$) in stochastic convex optimization. We jointly analyze the oracle complexity in both the local…
Zeroth-order methods are extensively used in machine learning applications where gradients are infeasible or expensive to compute, such as black-box attacks, reinforcement learning, and language model fine-tuning. Existing optimization…
This review presents modern gradient-free methods to solve convex optimization problems. By gradient-free methods, we mean those that use only (noisy) realizations of the objective value. We are motivated by various applications where…
We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…
We study (constrained) nonconvex (composite) optimization problems where the decision variables vector can be split into blocks of variables. Random block projection is a popular technique to handle this kind of problem for its remarkable…
This paper considers a consensus optimization problem, where all the nodes in a network, with access to the zeroth-order information of its local objective function only, attempt to cooperatively achieve a common minimizer of the sum of…
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…
We prove lower bounds for higher-order methods in smooth non-convex finite-sum optimization. Our contribution is threefold: We first show that a deterministic algorithm cannot profit from the finite-sum structure of the objective, and that…
In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…
Zeroth-order (derivative-free) optimization attracts a lot of attention in machine learning, because explicit gradient calculations may be computationally expensive or infeasible. To handle large scale problems both in volume and dimension,…