# p1: Better Prompt Optimization with Fewer Prompts

arXiv: https://arxiv.org/abs/2604.08801 · HTML: https://mlsanity.com/paper/2604.08801/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Generalizing Verifiable Instruction Following](https://mlsanity.com/paper/2507.02833/) (2025)
- [EvoPrompt: Connecting LLMs with Evolutionary Algorithms Yields Powerful Prompt Optimizers](https://mlsanity.com/paper/2309.08532/) (2023)
- [Instruction Induction: From Few Examples to Natural Language Task Descriptions](https://mlsanity.com/paper/2205.10782/) (2022)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [UPRISE: Universal Prompt Retrieval for Improving Zero-Shot Evaluation](https://mlsanity.com/paper/2303.08518/) (2023)
- [Trace is the Next AutoDiff: Generative Optimization with Rich Feedback, Execution Traces, and LLMs](https://mlsanity.com/paper/2406.16218/) (2024)
- [Prompt Curriculum Learning for Efficient LLM Post-Training](https://mlsanity.com/paper/2510.01135/) (2025)
- [One Prompt is not Enough: Automated Construction of a Mixture-of-Expert Prompts](https://mlsanity.com/paper/2407.00256/) (2024)
- [StablePrompt: Automatic Prompt Tuning using Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2410.07652/) (2024)
- [Prompt-R1: Collaborative Automatic Prompting Framework via End-to-end Reinforcement Learning](https://mlsanity.com/paper/2511.01016/) (2025)
- [Prompt-MII: Meta-Learning Instruction Induction for LLMs](https://mlsanity.com/paper/2510.16932/) (2025)
- [promptolution: A Unified, Modular Framework for Prompt Optimization](https://mlsanity.com/paper/2512.02840/) (2025)
- [Are My Optimized Prompts Compromised? Exploring Vulnerabilities of LLM-based Optimizers](https://mlsanity.com/paper/2510.14381/) (2025)

## Built on by (most cited first, 1 of 1)

- [SePO: Self-Evolving Prompt Agent for System Prompt Optimization](https://mlsanity.com/paper/2606.04465/) (2026)

## Abstract (arXiv)

Prompt optimization improves language models without updating their weights by searching for a better system prompt, but its effectiveness varies widely across tasks. We study what makes a task amenable to prompt optimization. We show that the reward variance across different system prompts can be decomposed into two components: variance among responses, which captures generation stochasticity, and variance among system prompts, which captures differences in system prompt quality. Prompt optimization succeeds when variance among system prompts is sufficiently large, but fails when variance among responses dominates the variance of the system prompts. Surprisingly, we further show that scaling to more user prompts can hurt optimization by reducing variance among system prompts, especially on heterogeneous datasets where different user prompts favor different system prompts. Motivated by this insight, we propose p1, a simple user prompt filtering method that selects a small subset of user prompts with high variance across candidate system prompts. This subset of user prompts allows one to distinguish a good system prompt from a bad one, making system optimization easier. Experiments on reasoning benchmarks show that p1 substantially improves prompt optimization over training on the full dataset and outperforms strong baselines such as GEPA. Notably, training on only two prompts from AIME 24 yields a system prompt that generalizes well to other reasoning benchmarks.