# Self-Evolving Algorithm-Design Agents: Escaping In-Context Evolutionary Stagnation via Population-Curated Policy Optimization

arXiv: https://arxiv.org/abs/2609.38757 · HTML: https://mlsanity.com/paper/2609.38757/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)
- Synthetic data and self-improvement for LLMs / [Self-evolving LLM agents](https://mlsanity.com/synth/self-evolving-llm-agents/)

## Builds on (most cited first, 30 of 30)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [KernelBench: Can LLMs Write Efficient GPU Kernels?](https://mlsanity.com/paper/2502.10517/) (2025)
- [A Comprehensive Survey of Self-Evolving AI Agents: A New Paradigm Bridging Foundation Models and Lifelong Agentic Systems](https://mlsanity.com/paper/2508.07407/) (2025)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [Learning to Discover at Test Time](https://mlsanity.com/paper/2601.16175/) (2026)
- [MemEvolve: Meta-Evolution of Agent Memory Systems](https://mlsanity.com/paper/2512.18746/) (2025)
- [ThetaEvolve: Test-time Learning on Open Problems](https://mlsanity.com/paper/2511.23473/) (2025)
- [CUDA-L1: Improving CUDA Optimization via Contrastive Reinforcement Learning](https://mlsanity.com/paper/2507.14111/) (2025)
- [RePO: Replay-Enhanced Policy Optimization](https://mlsanity.com/paper/2506.09340/) (2025)
- [Revisiting Group Relative Policy Optimization: Insights into On-Policy and Off-Policy Training](https://mlsanity.com/paper/2505.22257/) (2025)
- [Demystifying Domain-adaptive Post-training for Financial LLMs](https://mlsanity.com/paper/2501.04961/) (2025)
- [RL Grokking Recipe: How Does RL Unlock and Transfer New Algorithms in LLMs?](https://mlsanity.com/paper/2509.21016/) (2025)
- [Scientific Algorithm Discovery by Augmenting AlphaEvolve with Deep Research](https://mlsanity.com/paper/2510.06056/) (2025)
- [Just-In-Time Reinforcement Learning: Continual Learning in LLM Agents Without Gradient Updates](https://mlsanity.com/paper/2601.18510/) (2026)
- [Efficient RL Training for LLMs with Experience Replay](https://mlsanity.com/paper/2604.08706/) (2026)
- [KernelBench-Verified: Do LLM-Generated Kernels Actually Beat PyTorch?](https://mlsanity.com/paper/2607.16241/) (2026)
- [Structure-aware Domain Knowledge Injection for Large Language Models](https://mlsanity.com/paper/2407.16724/) (2024)
- [Self-evolving LLM agents with in-distribution Optimization](https://mlsanity.com/paper/2606.07367/) (2026)
- [MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling](https://mlsanity.com/paper/2606.13473/) (2026)
- [Advancing Automated Algorithm Design via Evolutionary Stagewise Design with LLMs](https://mlsanity.com/paper/2603.07970/) (2026)

## Abstract (arXiv)

Large language models are increasingly participating in complex real-world tasks in the form of algorithm-design agents, designing and refining algorithms. Many successful algorithm-design agents adopt pure in-context evolutionary frameworks, but they may quickly plateau in domains that require specialized knowledge. Parametric adaptation offers a way to internalize specialized knowledge, but conventional training requires abundant domain-specific corpora while high-quality algorithms are scarce in complex algorithm-design scenarios. In this paper, we propose sample-efficient parametric self-evolution where agents can explore and learn from self-generated algorithms. First, we characterize in-context evolutionary stagnation and analytically propose the Improvement Chain proposition, showing how learning successive self-generated algorithms can locally increase the likelihood of neighboring algorithms. Motivated by this local-transfer perspective, we further propose Population-Curated Policy Optimization (PCPO) to utilize a global population and a hybrid policy update scheme for retaining and reusing high-quality, diverse self-generated algorithms, shifting the policy towards stronger algorithms. In the task of learning rate schedule design for global placement in electronic design automation, trained only on 4 chip cases, PCPO outperforms the state-of-the-art in-context evolutionary methods (e.g., OpenEvolve and ShinkaEvolve) on average across 16 chip cases. With an 8B-size base model, PCPO achieves competitive performance compared to frontier closed-source models such as GPT-5.5. PCPO also reduces inference-time token cost by internalizing grounded domain knowledge and prompt distillation. Moreover, PCPO achieves significant speedups on four GPU kernel designs, with an average of 8.27× speedup against the PyTorch Eager baseline.