Elucidating Subspace Perturbation in Zeroth-Order Optimization: Theory and Practice at Scale
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908375869030400 |
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| author | Park, Sihwan Yun, Jihun Kim, SungYub Kundu, Souvik Yang, Eunho |
| author_facet | Park, Sihwan Yun, Jihun Kim, SungYub Kundu, Souvik Yang, Eunho |
| contents | Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods, particularly for black-box optimization and large language model (LLM) fine-tuning. However, ZO methods often suffer from slow convergence due to high-variance stochastic gradient estimators. While subspace perturbations, such as sparsity and low-rank constraints, have been explored to mitigate this issue, their effectiveness remains poorly understood. In this work, we develop a \emph{unified theoretical framework} that analyzes both the convergence and generalization properties of ZO optimization under subspace perturbations. We show that high dimensionality is the primary bottleneck and introduce the notion of \textit{subspace alignment} to explain how the subspace perturbations reduce gradient noise and accelerate convergence. Our analysis further shows that a broad class of subspace perturbations exhibits a similar convergence rate, motivating us to prioritize practical considerations in real-world algorithm design. Building on these insights, we propose an efficient ZO method using block coordinate descent (MeZO-BCD), which perturbs and updates only a subset of parameters at each step. Extensive experiments show that MeZO-BCD significantly accelerates optimization, achieving up to $\mathbf{\times2.77}$ speedup in wall-clock time over MeZO on OPT-13B, while maintaining comparable iteration complexity and fine-tuning performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elucidating Subspace Perturbation in Zeroth-Order Optimization: Theory and Practice at Scale Park, Sihwan Yun, Jihun Kim, SungYub Kundu, Souvik Yang, Eunho Machine Learning Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods, particularly for black-box optimization and large language model (LLM) fine-tuning. However, ZO methods often suffer from slow convergence due to high-variance stochastic gradient estimators. While subspace perturbations, such as sparsity and low-rank constraints, have been explored to mitigate this issue, their effectiveness remains poorly understood. In this work, we develop a \emph{unified theoretical framework} that analyzes both the convergence and generalization properties of ZO optimization under subspace perturbations. We show that high dimensionality is the primary bottleneck and introduce the notion of \textit{subspace alignment} to explain how the subspace perturbations reduce gradient noise and accelerate convergence. Our analysis further shows that a broad class of subspace perturbations exhibits a similar convergence rate, motivating us to prioritize practical considerations in real-world algorithm design. Building on these insights, we propose an efficient ZO method using block coordinate descent (MeZO-BCD), which perturbs and updates only a subset of parameters at each step. Extensive experiments show that MeZO-BCD significantly accelerates optimization, achieving up to $\mathbf{\times2.77}$ speedup in wall-clock time over MeZO on OPT-13B, while maintaining comparable iteration complexity and fine-tuning performance. |
| title | Elucidating Subspace Perturbation in Zeroth-Order Optimization: Theory and Practice at Scale |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2501.19099 |