# Open-Ended Task Discovery via Bayesian Optimization

arXiv: https://arxiv.org/abs/2605.07572 · HTML: https://mlsanity.com/paper/2605.07572/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 80 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 16 of 16)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [Freeze-Thaw Bayesian Optimization](https://mlsanity.com/paper/1406.3896/) (2014)
- [CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimization](https://mlsanity.com/paper/2510.14150/) (2025)
- [How to Correctly Report LLM-as-a-Judge Evaluations](https://mlsanity.com/paper/2511.21140/) (2025)
- [In-Context Learning Is Provably Bayesian Inference: A Generalization Theory for Meta-Learning](https://mlsanity.com/paper/2510.10981/) (2025)
- [Accelerating Scientific Discovery with Autonomous Goal-evolving Agents](https://mlsanity.com/paper/2512.21782/) (2025)
- [Can LLMs Beat Classical Hyperparameter Optimization Algorithms? A Study on autoresearch](https://mlsanity.com/paper/2603.24647/) (2026)
- [Bayesian Optimization for Building Social-Influence-Free Consensus](https://mlsanity.com/paper/2502.07166/) (2025)
- [Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities](https://mlsanity.com/paper/2603.10396/) (2026)
- [Natural Evolutionary Search meets Probabilistic Numerics](https://mlsanity.com/paper/2507.07288/) (2025)
- [Consequences of Kernel Regularity for Bandit Optimization](https://mlsanity.com/paper/2512.05957/) (2025)

## Built on by (most cited first, 2 of 2)

- [Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs](https://mlsanity.com/paper/2605.10385/) (2026)
- [Open-ended Scientific Discovery with Possibilistic Reasoning](https://mlsanity.com/paper/2610.11289/) (2026)

## Abstract (arXiv)

When applying Bayesian optimization (BO) to scientific workflow, a major yet often overlooked source of uncertainty is the task itself -- namely, what to optimize and how to evaluate it -- which can evolve as evidence accumulates. We introduce Generate-Select-Refine (GSR), a open-ended BO framework that alternates between task generation and task optimization. Starting from a user-provided seed task, GSR generates new tasks in a coarse-to-fine manner while a task-acquisition function schedules optimization. Asymptotically, it concentrates evaluations on the best task, incurring only logarithmic regret overhead relative to single-task BO. We apply GSR to new product development, chemical synthesis scaling, algorithm analysis, and patent repurposing, where it outperforms existing LLM-based optimizers.