The Importance of Directional Feedback for LLM-based Optimizers

TL;DR

This paper demonstrates that large language models can effectively serve as interactive optimizers in natural language and numerical feedback settings, especially when provided with directional feedback, leading to more stable and efficient optimization.

Contribution

The paper introduces a novel LLM-based optimizer that synthesizes directional feedback from historical data, improving optimization stability and efficiency in various tasks.

Findings

LLMs perform better with directional feedback.

The proposed optimizer outperforms existing techniques.

It is effective in diverse optimization tasks.

Abstract

We study the potential of using large language models (LLMs) as an interactive optimizer for solving maximization problems in a text space using natural language and numerical feedback. Inspired by the classical optimization literature, we classify the natural language feedback into directional and non-directional, where the former is a generalization of the first-order feedback to the natural language space. We find that LLMs are especially capable of optimization when they are provided with {directional feedback}. Based on this insight, we design a new LLM-based optimizer that synthesizes directional feedback from the historical optimization trace to achieve reliable improvement over iterations. Empirically, we show our LLM-based optimizer is more stable and efficient in solving optimization problems, from maximizing mathematical functions to optimizing prompts for writing poems, compared with existing techniques.