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On the Convergence of Zeroth-Order Federated Tuning for Large Language Models

Zhenqing Ling, Daoyuan Chen, Liuyi Yao, Yaliang Li, Ying Shen

TL;DR

This study is the first to examine the theoretical underpinnings of FedMeZO in the context of LLMs, tackling key questions regarding the influence of large parameter spaces on optimization behavior, the establishment of convergence properties, and the identification of critical parameters for convergence to inform personalized federated strategies.

Abstract

The confluence of Federated Learning (FL) and Large Language Models (LLMs) is ushering in a new era in privacy-preserving natural language processing. However, the intensive memory requirements for fine-tuning LLMs pose significant challenges, especially when deploying on clients with limited computational resources. To circumvent this, we explore the novel integration of Memory-efficient Zeroth-Order Optimization within a federated setting, a synergy we term as FedMeZO. Our study is the first to examine the theoretical underpinnings of FedMeZO in the context of LLMs, tackling key questions regarding the influence of large parameter spaces on optimization behavior, the establishment of convergence properties, and the identification of critical parameters for convergence to inform personalized federated strategies. Our extensive empirical evidence supports the theory, showing that FedMeZO not only converges faster than traditional first-order methods such as FedAvg but also significantly reduces GPU memory usage during training to levels comparable to those during inference. Moreover, the proposed personalized FL strategy that is built upon the theoretical insights to customize the client-wise learning rate can effectively accelerate loss reduction. We hope our work can help to bridge theoretical and practical aspects of federated fine-tuning for LLMs, thereby stimulating further advancements and research in this area.

On the Convergence of Zeroth-Order Federated Tuning for Large Language Models

TL;DR

This study is the first to examine the theoretical underpinnings of FedMeZO in the context of LLMs, tackling key questions regarding the influence of large parameter spaces on optimization behavior, the establishment of convergence properties, and the identification of critical parameters for convergence to inform personalized federated strategies.

Abstract

The confluence of Federated Learning (FL) and Large Language Models (LLMs) is ushering in a new era in privacy-preserving natural language processing. However, the intensive memory requirements for fine-tuning LLMs pose significant challenges, especially when deploying on clients with limited computational resources. To circumvent this, we explore the novel integration of Memory-efficient Zeroth-Order Optimization within a federated setting, a synergy we term as FedMeZO. Our study is the first to examine the theoretical underpinnings of FedMeZO in the context of LLMs, tackling key questions regarding the influence of large parameter spaces on optimization behavior, the establishment of convergence properties, and the identification of critical parameters for convergence to inform personalized federated strategies. Our extensive empirical evidence supports the theory, showing that FedMeZO not only converges faster than traditional first-order methods such as FedAvg but also significantly reduces GPU memory usage during training to levels comparable to those during inference. Moreover, the proposed personalized FL strategy that is built upon the theoretical insights to customize the client-wise learning rate can effectively accelerate loss reduction. We hope our work can help to bridge theoretical and practical aspects of federated fine-tuning for LLMs, thereby stimulating further advancements and research in this area.
Paper Structure (52 sections, 11 theorems, 65 equations, 10 figures, 8 tables)

This paper contains 52 sections, 11 theorems, 65 equations, 10 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Background and Related Works
  4. Federated Fine-Tuning of Large Language Models.
  5. Zeroth-Order Optimization in Federated Learning.
  6. Problem Formulation
  7. Federated Learning.
  8. Zeroth-Order Optimization.
  9. The FedMeZO Algorithm.
  10. Lemmas and Assumptions
  11. Main results
  12. Convergence Analysis in $\text{i.i.d.}$ Case
  13. Convergence Analysis in Non-i.i.d Case
  14. Implications
  15. Proof Outline
  16. ...and 37 more sections

Key Result

Lemma 2.2

(Unbiased Gradient Estimator) The two-point zeroth-order gradient estimator described in Eq. eq:pre_two_point_estimator_def is an unbiased estimator of the true gradient, that is,

Figures (10)

  • Figure 1: Convergence comparison of FedMeZO and BP-based FedAvg. More results are in Appendix \ref{['appendix:exp_main_convergence_app']}.
  • Figure 2: Effects of different perturbation scales $\mu$. More results are in Appendix \ref{['appendix:exp_impact_mu']}.
  • Figure 3: Effects of different local iteration steps $H$. More results are in Appendix \ref{['appendix:exp_impact_H']}.
  • Figure 4: Comparison of different strategies of learning rate adjustment. "Default" indicates non-personalized case, and "Round-wise Loss", "Five-round Loss" and "Model Update Difference" indicate three signal quantities leveraged.
  • Figure 5: Phenomenon of loss surge due to larger learning rates.
  • ...and 5 more figures

Theorems & Definitions (13)

  • Definition 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Theorem 3.1
  • Corollary 3.2
  • Corollary 3.3
  • Theorem 3.4
  • Corollary 3.5
  • Corollary 3.6
  • Proposition 3.7
  • ...and 3 more