Derivative-free stochastic optimization via adaptive sampling strategies

Journal Article · Wed Jan 01 00:00:00 EST 2025 · Optimization Methods and Software

DOI:https://doi.org/10.1080/10556788.2025.2547397· OSTI ID:2998214

Bollapragada, Raghu; Karamanli, Cem; Wild, Stefan M

In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: US Department of Energy; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Scientific User Facilities Division (SC-22.3 )
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 2998214
• Journal Information: Optimization Methods and Software, Journal Name: Optimization Methods and Software Journal Issue: ahead-of-print Vol. ahead-of-print
• Country of Publication: United States
• Language: English

Related Subjects

Adaptive sampling
common random numbers
derivative-free optimization
gradient approximations