Designing Meta-Prompts for Stable and Effective LLM Optimization

:::info Authors:

(1) Chengrun Yang, Google DeepMind and Equal contribution;

(2) Xuezhi Wang, Google DeepMind;

(3) Yifeng Lu, Google DeepMind;

(4) Hanxiao Liu, Google DeepMind;

(5) Quoc V. Le, Google DeepMind;

(6) Denny Zhou, Google DeepMind;

(7) Xinyun Chen, Google DeepMind and Equal contribution.

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Abstract and 1. Introduction

2 Opro: Llm as the Optimizer and 2.1 Desirables of Optimization by Llms

2.2 Meta-Prompt Design

3 Motivating Example: Mathematical Optimization and 3.1 Linear Regression

3.2 Traveling Salesman Problem (TSP)

4 Application: Prompt Optimization and 4.1 Problem Setup

4.2 Meta-Prompt Design

5 Prompt Optimization Experiments and 5.1 Evaluation Setup

5.2 Main Results

5.3 Ablation Studies

5.4 Overfitting Analysis in Prompt Optimization and 5.5 Comparison with Evoprompt

6 Related Work

7 Conclusion, Acknowledgments and References

A Some Failure Cases

B Prompting Formats for Scorer Llm

C Meta-Prompts and C.1 Meta-Prompt for Math Optimization

C.2 Meta-Prompt for Prompt Optimization

D Prompt Optimization Curves on the Remaining Bbh Tasks

E Prompt Optimization on Bbh Tasks – Tabulated Accuracies and Found Instructions

As the input to the LLM that acts as the optimizer, the meta-prompt contains the following two essential parts.

\ Optimization problem description. The first part is the text description of the optimization problem, including the objective function and solution constraints. For example, for prompt optimization, the LLM can be instructed to “generate a new instruction that achieves a higher accuracy”, and we denote such instructions in the meta-prompt as meta-instructions. We can also provide customized meta-instructions as an informal regularization of the generated solutions, such as “the instruction should be concise and generally applicable”.

\ Optimization trajectory. Besides understanding natural language instructions, LLMs are also shown to be able to recognize patterns from in-context demonstrations (Wei et al., 2023; Madaan & Yazdanbakhsh, 2022; Mirchandani et al., 2023). Our meta-prompt makes use of this property and instructs the LLM to leverage the optimization trajectory for generating new solutions. Specifically, the optimization trajectory includes past solutions paired with their optimization scores, sorted in the ascending order. Including optimization trajectory in the meta-prompt allows the LLM to identify similarities of solutions with high scores, encouraging the LLM to build upon existing good solutions to construct potentially better ones without the need of explicitly defining how the solution should be updated.

At the solution generation step, the LLM generates new solutions with the meta-prompt as input. The following are the key optimization challenges we address in this stage.

\ Optimization stability. In the optimization process, not all solutions achieve high scores and monotonically improve over prior ones. Due to the sensitivity of in-context learning to the prompt, LLM output can be drastically affected by low-quality solutions in the input optimization trajectory, especially at the beginning when the solution space has not been adequately explored. This sometimes results in optimization instability and large variance. To improve stability, we prompt the LLM to generate multiple solutions at each optimization step, allowing the LLM to simultaneously explore multiple possibilities and quickly discover promising directions to move forward.

\ Exploration-exploitation trade-off. We tune the LLM sampling temperature to balance between exploration and exploitation. A lower temperature encourages the LLM to exploit the solution space around the previously found solutions and make small adaptations, while a high temperature allows the LLM to more aggressively explore solutions that can be notably different.

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:::info This paper is available on arxiv under CC0 1.0 DEED license.

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