# Optimal Stopping of Self-Refining Foundation Models

arXiv: https://arxiv.org/abs/2608.10729 · HTML: https://mlsanity.com/paper/2608.10729/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 11 Aug 2026.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Towards End-to-End Automation of AI Research](https://mlsanity.com/paper/2606.15497/) (2026)
- [LLM-Based Multi-Agent Systems for Software Engineering: Literature Review, Vision and the Road Ahead](https://mlsanity.com/paper/2404.04834/) (2024)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [ISR-LLM: Iterative Self-Refined Large Language Model for Long-Horizon Sequential Task Planning](https://mlsanity.com/paper/2308.13724/) (2023)
- [EffiBench: Benchmarking the Efficiency of Automatically Generated Code](https://mlsanity.com/paper/2402.02037/) (2024)
- [A Theoretical Understanding of Self-Correction through In-context Alignment](https://mlsanity.com/paper/2405.18634/) (2024)
- [Partially Observed Markov Decision Processes. Problem Sets and Internet Supplement](https://mlsanity.com/paper/1604.08127/) (2016)
- [EffiLearner: Enhancing Efficiency of Generated Code via Self-Optimization](https://mlsanity.com/paper/2405.15189/) (2024)
- [ChronosX: Adapting Pretrained Time Series Models with Exogenous Variables](https://mlsanity.com/paper/2503.12107/) (2025)
- [Procedural Content Generation in Games: A Survey with Insights on Emerging LLM Integration](https://mlsanity.com/paper/2410.15644/) (2024)
- [Intrusion Prevention through Optimal Stopping](https://mlsanity.com/paper/2111.00289/) (2021)
- [Stop When Enough: Adaptive Early-Stopping for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2510.10103/) (2025)
- [Automated Security Response through Online Learning with Adaptive Conjectures](https://mlsanity.com/paper/2402.12499/) (2024)
- [Incident Response Planning Using a Lightweight Large Language Model with Reduced Hallucination](https://mlsanity.com/paper/2508.05188/) (2025)
- [LLMs can learn self-restraint through iterative self-reflection](https://mlsanity.com/paper/2405.13022/) (2024)
- [Adaptive Network Security Policies via Belief Aggregation and Rollout](https://mlsanity.com/paper/2507.15163/) (2025)

## Abstract (arXiv)

Foundation models can improve their outputs through a self-refinement process driven by external feedback. In this process, the model is embedded in an iterative loop where it generates outputs, receives feedback from verifiers, and refines its responses through in-context learning. Following a novel approach, we formalize this process as an optimal stopping problem where the number of refinement iterations is decided based on expected improvement relative to cost. We derive optimal stopping policies and show that they can be efficiently computed through stochastic approximation. To evaluate our approach experimentally, we apply it to a coding benchmark for foundation models. The empirical results show that our stopping policies are significantly more cost-efficient than stopping policies proposed in prior work.