arXiv research

Zeroth-order optimization methods lack inherent privacy guarantees.

Zeroth-order methods favor flat minima in machine learning.

In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle constrained optimization, we first propose generalizations of the conditional g…

New method for zeroth-order stochastic gradient algorithms provides confidence intervals.

We propose a method for zeroth order stochastic convex optimization that attains the suboptimality rate of $\tilde{\mathcal{O}}(n^{7}T^{-1/2})$ after $T$ queries for a convex bounded function $f:{\mathbb R}^n\to{\mathbb R}$. The method is based on a random walk (the \emph{Ball Walk}) on the epigraph of the function. Th…

Zeroth-order optimization is an important research topic in machine learning. In recent years, it has become a key tool in black-box adversarial attack to neural network based image classifiers. However, existing zeroth-order optimization algorithms rarely extract second-order information of the model function. In this…

Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving complex machine learning problems, where gradients of the objective functions are not available or computationally prohibitive. Recently, although many zeroth-order methods have been developed, these approaches still…

Book covers tools for zeroth-order convex optimisation.

Improves zeroth-order optimization for private machine learning with public data.

Proximal gradient method has been playing an important role to solve many machine learning tasks, especially for the nonsmooth problems. However, in some machine learning problems such as the bandit model and the black-box learning problem, proximal gradient method could fail because the explicit gradients of these pro…

A new method for MARL with partial observations reduces communication overhead.

New optimization method improves generalization across various tasks.

New method improves zeroth-order stochastic optimization with adaptive sampling.

We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimate…

Alternating direction method of multipliers (ADMM) is a popular optimization tool for the composite and constrained problems in machine learning. However, in many machine learning problems such as black-box attacks and bandit feedback, ADMM could fail because the explicit gradients of these problems are difficult or in…

ConMeZO speeds up zeroth-order optimization for large language models.

New method uses zeroth-order queries to approximate proximal sampling efficiently.

This paper reviews zeroth-order optimization in signal processing and machine learning.

Two types of zeroth-order stochastic algorithms have recently been designed for nonconvex optimization respectively based on the first-order techniques SVRG and SARAH/SPIDER. This paper addresses several important issues that are still open in these methods. First, all existing SVRG-type zeroth-order algorithms suffer …

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossibl…

Paper proposes ZO-NGD for more efficient black-box attacks.

ZOSPI improves RL policies with global value function exploitation.

New adaptive methods solve weakly convex stochastic optimization problems.

New algorithm reduces regret in stochastic bandit convex optimization.

Simplifies noisy convex optimization with a new algorithm.

New Hessian estimators for Riemannian manifolds with reduced bias.

Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.

In this paper, we design and analyze a new zeroth-order online algorithm, namely, the zeroth-order online alternating direction method of multipliers (ZOO-ADMM), which enjoys dual advantages of being gradient-free operation and employing the ADMM to accommodate complex structured regularizers. Compared to the first-ord…

We present $\textit{Free-MESSAGE}^{p}$, the first zeroth-order algorithm for (weakly-)convex mean-semideviation-based risk-aware learning, which is also the first three-level zeroth-order compositional stochastic optimization algorithm whatsoever. Using a non-trivial extension of Nesterov's classical results on Gaussia…

Optimal algorithms for Riemannian optimization with reduced complexity.

Sparse perturbations improve convergence in SZO methods for faster training.

DPZero fine-tunes large models privately without backpropagation.

LAZO reduces query complexity and variance in ZO methods.

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 many applications in which the local objective function is the sum of smooth but po…

Method extracts features from signals for classification with explainability.

Paper tackles gradient-free minimax optimization with variance reduction for faster convergence.

Paper proposes algorithms for solving nonconvex-nonconcave problems with complexity guarantees.

New algorithms solve complex minimax problems without needing derivatives.

This paper analyzes and guarantees convergence of prior-guided ZO algorithms.

New stability conditions for ZO methods reveal unique regularization effects.

New algorithm reduces dimensionality in stochastic optimization.

Efficient algorithm for zeroth-order bandit convex optimization with bounds on regret.

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationar…

A new algorithm for optimizing huge-scale black-box problems with reduced memory usage.

Stochastic zeroth-order (SZO), or gradient-free, optimization allows to optimize arbitrary functions by relying only on function evaluations under parameter perturbations, however, the iteration complexity of SZO methods suffers a factor proportional to the dimensionality of the perturbed function. We show that in scen…

In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first consider a …

We provide evidence for the conjecture that the Wodzicki-Chern classes vanish for all bundles with the group Z of invertible zeroth order pseudodifferential operators as structure group. In particular, we prove this vanishing if the structure group reduces to pseudodifferential operators with leading order symbol the i…

LORENZA improves LLM fine-tuning efficiency and generalization.