Two Optimizers Are Better Than One: LLM Catalyst for Enhancing Gradient-Based Optimization

Learning a skill generally relies on both practical experience by doer and insightful high-level guidance by instructor. Will this strategy also work well for solving complex non-convex optimization problems? Here, a common gradient-based optimizer acts like a disciplined doer, making locally optimal update at each step. Recent methods utilize large language models (LLMs) to optimize solutions for concrete problems by inferring from natural language instructions, akin to a high-level instructor. In this paper, we show that these two optimizers are complementary to each other, suggesting a collaborative optimization approach. The gradient-based optimizer and LLM-based optimizer are combined in an interleaved manner. We instruct LLMs using task descriptions and timely optimization trajectories recorded during gradient-based optimization. Inferred results from LLMs are used as restarting points for the next stage of gradient optimization. By leveraging both the locally rigorous gradient-based optimizer and the high-level deductive LLM-based optimizer, our combined optimization method consistently yields improvements over competitive baseline prompt tuning methods. Our results demonstrate the synergistic effect of conventional gradient-based optimization and the inference ability of LLMs. The code is released at https://github.com/guozix/LLM-catalyst.