Importance of Directional Feedback for LLM-based Optimizers

Allen Nie, Ching-An Cheng, Andrey Kolobov, Adith Swaminathan

Keywords: constrained optimization, prompt optimization

Abstract:

We study the potential of using large language models (LLMs) as an interactive
optimizer for solving maximization problems on 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.

Submission Number: 104