This paper explores the potential of using large language models (LLMs) as interactive optimizers for solving maximization problems in text space, particularly focusing on the importance of directional feedback. The authors classify natural language feedback into directional and non-directional, where directional feedback is a generalization of first-order feedback to the natural language space. They find that LLMs perform better when provided with directional feedback and design a new LLM-based optimizer that synthesizes this feedback from historical optimization traces to achieve reliable improvement over iterations. Empirical results show that their LLM-based optimizer is more stable and efficient in solving optimization problems, including maximizing mathematical functions and optimizing prompts for writing poems, compared to existing techniques. The paper also discusses the role of feedback in LLM-based text optimization and highlights the importance of directional feedback in achieving effective optimization.This paper explores the potential of using large language models (LLMs) as interactive optimizers for solving maximization problems in text space, particularly focusing on the importance of directional feedback. The authors classify natural language feedback into directional and non-directional, where directional feedback is a generalization of first-order feedback to the natural language space. They find that LLMs perform better when provided with directional feedback and design a new LLM-based optimizer that synthesizes this feedback from historical optimization traces to achieve reliable improvement over iterations. Empirical results show that their LLM-based optimizer is more stable and efficient in solving optimization problems, including maximizing mathematical functions and optimizing prompts for writing poems, compared to existing techniques. The paper also discusses the role of feedback in LLM-based text optimization and highlights the importance of directional feedback in achieving effective optimization.