Beyond Value Functions: Single-Loop Bilevel Optimization under Flatness Conditions

TL;DR

This paper introduces a novel single-loop, value-function-free bilevel optimization algorithm that is more computationally efficient and suitable for large language model fine-tuning, supported by theoretical convergence guarantees.

Contribution

It proposes a fully first-order, flatness condition-based algorithm that removes nested loops, improving efficiency in large-scale bilevel problems like LLM fine-tuning.

Findings

The algorithm converges under a relaxed flatness condition.

It outperforms existing methods in computational efficiency.

Experimental results validate its effectiveness in various applications.

Abstract

Bilevel optimization, a hierarchical optimization paradigm, has gained significant attention in a wide range of practical applications, notably in the fine-tuning of generative models. However, due to the nested problem structure, most existing algorithms require either the Hessian vector calculation or the nested loop updates, which are computationally inefficient in large language model (LLM) fine-tuning. In this paper, building upon the fully first-order penalty-based approach, we propose an efficient value function-free (PBGD-Free) algorithm that eliminates the loop of solving the lower-level problem and admits fully single-loop updates. Inspired by the landscape analysis of representation learning-based LLM fine-tuning problem, we propose a relaxed flatness condition for the upper-level function and prove the convergence of the proposed value-function-free algorithm. We test the performance of the proposed algorithm in various applications and demonstrate its superior computational efficiency over the state-of-the-art bilevel methods.