# PACE: Anytime-Valid Acceptance Tests for Self-Evolving Agents

arXiv: https://arxiv.org/abs/2606.08106 · HTML: https://mlsanity.com/paper/2606.08106/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 6 Jun 2026.

## Builds on (most cited first, 24 of 24)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [Agent Workflow Memory](https://mlsanity.com/paper/2409.07429/) (2024)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [TextGrad: Automatic "Differentiation" via Text](https://mlsanity.com/paper/2406.07496/) (2024)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [The Ladder: A Reliable Leaderboard for Machine Learning Competitions](https://mlsanity.com/paper/1502.04585/) (2015)
- [Can Large Reasoning Models Self-Train?](https://mlsanity.com/paper/2505.21444/) (2025)
- [There are natural scores: Full comment on Shafer, "Testing by betting: A strategy for statistical and scientific communication"](https://mlsanity.com/paper/2102.05569/) (2021)
- [G"odel Agent: A Self-Referential Agent Framework for Recursive Self-Improvement](https://mlsanity.com/paper/2410.04444/) (2024)
- [Online control of the false discovery rate with decaying memory](https://mlsanity.com/paper/1710.00499/) (2017)

## Built on by (most cited first, 13 of 13)

- [Recursive Experiential-Working Memory Evolution for Long-Horizon Agent Harnesses](https://mlsanity.com/paper/2608.24876/) (2026)
- [A Theory of Reliable Self-Evolution for Agent Harnesses](https://mlsanity.com/paper/2609.08175/) (2026)
- [Pay Only for Disagreement: Certified No-Regression Verdicts for Model Updates with Matching Label-Complexity Bounds](https://mlsanity.com/paper/2609.17560/) (2026)
- [When Is Enough Enough in Self-Evolving LLM Systems?](https://mlsanity.com/paper/2610.04756/) (2026)
- [Discovering Translation-Worthy Languages with E-Values](https://mlsanity.com/paper/2609.06593/) (2026)
- [Local Edits, Global Ripples: Replay-Informed Policy Adaptation for Workflow Synthesis](https://mlsanity.com/paper/2609.12127/) (2026)
- [Propose, Don't Judge: An Anytime-Valid Referee for LLM Agents That Mine Investment Factors](https://mlsanity.com/paper/2609.27051/) (2026)
- [Which Self-Improvements Should We Trust? Reliable Self-Improvement When Agents Reuse Their Benchmarks](https://mlsanity.com/paper/2609.33180/) (2026)
- [EvoSteer: Online Self-Evolving Graph Orchestration via Reference-Anchored Credit Assignment](https://mlsanity.com/paper/2609.38661/) (2026)
- [MemCodex: Self-Programming Hierarchical Memory for Language Agents](https://mlsanity.com/paper/2609.39765/) (2026)
- [What Does a Harness Repair? A Preregistered Study of Visibility, Baseline Adequacy and Evaluation Defects](https://mlsanity.com/paper/2610.05533/) (2026)
- [The Winner's Curse in LLM Self-Improvement Loops: Selection Noise, Lock-in, and Acceptance Rules](https://mlsanity.com/paper/2610.09239/) (2026)
- [Cortex: Measurement-Gated Evolution and Pruning of Coding-Agent Skills and Rules](https://mlsanity.com/paper/2610.14216/) (2026)

## Abstract (arXiv)

Self-evolving agents improve by repeatedly proposing changes to their own prompts, skills, or workflows and keeping those that score higher on a small held-out set. Almost all effort has gone into the proposer that generates candidates; we argue the weak point is the acceptor, the rule that decides whether to commit a change. Applied hundreds of times against the same noisy dev estimate, the ubiquitous "keep it if the score went up" rule is uncontrolled adaptive multiple testing: the agent effectively p-hacks itself, accumulating false commits that make it churn and drift rather than improve. We recast committing as a sequential hypothesis test and propose PACE (Paired Anytime-valid Commit Evaluation), a training-free, anytime-valid commit gate. Each candidate is compared to the incumbent on identical instances and committed only when a testing-by-betting e-process accumulates decisive evidence, stopping early to save evaluations and controlling each candidate's false-commit probability at a user-set level even under optional stopping (a per-decision guarantee). On Qwen2.5 agents (0.5B-3B) self-evolving at the prompt level on GSM8K, SVAMP, and ARC-Challenge, greedy acceptance commits 30-42% false and 10-33% harmful edits when a genuine improvement is hidden among noisy proposals, while PACE commits the real one and essentially nothing else, matching greedy's held-out accuracy at sharply lower variance and about 18% lower evaluation cost. With no real gain available, greedy commits 13-21 spurious self-modifications per run (72-100% false) and degrades the most fragile agent by 4.9 points, while PACE holds at baseline. Reliability of self-evolution depends on the acceptor, not only on the proposer.