Stochastic Subspace Descent Accelerated via Bi-fidelity Line Search

• URL: http://arxiv.org/abs/2505.00162v1
• Date: Wed, 30 Apr 2025 20:17:35 GMT
• Title: Stochastic Subspace Descent Accelerated via Bi-fidelity Line Search
• Authors: Nuojin Cheng, Alireza Doostan, Stephen Becker,
• Abstract summary: This work introduces the bi-fidelity subspace descent (BF-SSD) algorithm, a novel zeroth-order optimization method.<n> BF-SSD consistently achieves superior optimization performance while requiring significantly fewer high-fidelity evaluations.<n>This study highlights the efficacy of integrating bi-fidelity within zeroth-order optimization, positioning BF-SSD as a promising and computationally efficient approach.
• Score: 2.2940141855172036
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Efficient optimization remains a fundamental challenge across numerous scientific and engineering domains, especially when objective function and gradient evaluations are computationally expensive. While zeroth-order optimization methods offer effective approaches when gradients are inaccessible, their practical performance can be limited by the high cost associated with function queries. This work introduces the bi-fidelity stochastic subspace descent (BF-SSD) algorithm, a novel zeroth-order optimization method designed to reduce this computational burden. BF-SSD leverages a bi-fidelity framework, constructing a surrogate model from a combination of computationally inexpensive low-fidelity (LF) and accurate high-fidelity (HF) function evaluations. This surrogate model facilitates an efficient backtracking line search for step size selection, for which we provide theoretical convergence guarantees under standard assumptions. We perform a comprehensive empirical evaluation of BF-SSD across four distinct problems: a synthetic optimization benchmark, dual-form kernel ridge regression, black-box adversarial attacks on machine learning models, and transformer-based black-box language model fine-tuning. Numerical results demonstrate that BF-SSD consistently achieves superior optimization performance while requiring significantly fewer HF function evaluations compared to relevant baseline methods. This study highlights the efficacy of integrating bi-fidelity strategies within zeroth-order optimization, positioning BF-SSD as a promising and computationally efficient approach for tackling large-scale, high-dimensional problems encountered in various real-world applications.

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