Zeroth-Order Regularized Optimization (ZORO): Approximately Sparse Gradients and Adaptive Sampling

Abstract

We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using (possibly noisy) evaluations of the function. Such optimization is also called derivative-free, zeroth-order, or black-box optimization. We propose a new $\text{Z}$eroth-$\text{O}$rder $\text{R}$egularized $\text{O}$ptimization method, dubbed ZORO. When the underlying gradient is approximately sparse at an iterate, ZORO needs very few objective function evaluations to obtain a new iterate that decreases the objective function. We achieve this with an adaptive, randomized gradient estimator, followed by an inexact proximal-gradient scheme. Under a novel approximately sparse gradient assumption and various different convex settings, we show the (theoretical and empirical) convergence rate of ZORO is only logarithmically dependent on the problem dimension. Numerical experiments show that ZORO outperforms the existing methods with similar assumptions, on both synthetic and real datasets.

References in corpus (7)

• Practical Bayesian Optimization of Machine Learning Algorithms
• Evolution Strategies as a Scalable Alternative to Reinforcement Learning
• Hybrid Deterministic-Stochastic Methods for Data Fitting
• Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization
• Simple random search provides a competitive approach to reinforcement learning
• Stochastic Zeroth-order Optimization in High Dimensions
• ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization

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• Curvature-Aware Derivative-Free Optimization
• Explainable Adversarial Attacks on Coarse-to-Fine Classifiers
• Statistical Inference for Polyak-Ruppert Averaged Zeroth-order Stochastic Gradient Algorithm
• A Dimension-Insensitive Algorithm for Stochastic Zeroth-Order Optimization