# Cross-Epoch Adaptive Rollout Optimization for RL Post-Training

arXiv: https://arxiv.org/abs/2606.05606 · HTML: https://mlsanity.com/paper/2606.05606/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 37 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Online Difficulty Filtering for Reasoning Oriented Reinforcement Learning](https://mlsanity.com/paper/2504.03380/) (2025)
- [CPPO: Accelerating the Training of Group Relative Policy Optimization-Based Reasoning Models](https://mlsanity.com/paper/2503.22342/) (2025)
- [Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning](https://mlsanity.com/paper/2504.13818/) (2025)
- [Sample More to Think Less: Group Filtered Policy Optimization for Concise Reasoning](https://mlsanity.com/paper/2508.09726/) (2025)
- [Dual Mirror Descent for Online Allocation Problems](https://mlsanity.com/paper/2002.10421/) (2020)
- [Fast Algorithms for Online Stochastic Convex Programming](https://mlsanity.com/paper/1410.7596/) (2014)
- [Online Linear Programming: Dual Convergence, New Algorithms, and Regret Bounds](https://mlsanity.com/paper/1909.05499/) (2019)
- [SPEED-RL: Faster Training of Reasoning Models via Online Curriculum Learning](https://mlsanity.com/paper/2506.09016/) (2025)
- [Non-stationary Bandits with Knapsacks](https://mlsanity.com/paper/2205.12427/) (2022)
- [Uniformly bounded regret in the multi-secretary problem](https://mlsanity.com/paper/1710.07719/) (2017)
- [Primal Beats Dual on Online Packing LPs in the Random-Order Model](https://mlsanity.com/paper/1311.2578/) (2013)
- [Train Less, Learn More: Adaptive Efficient Rollout Optimization for Group-Based Reinforcement Learning](https://mlsanity.com/paper/2602.14338/) (2026)
- [Degeneracy is OK: Logarithmic Regret for Network Revenue Management with Indiscrete Distributions](https://mlsanity.com/paper/2210.07996/) (2022)
- [CoBA-RL: Capability-Oriented Budget Allocation for Reinforcement Learning in LLMs](https://mlsanity.com/paper/2602.03048/) (2026)
- [VADE: Variance-Aware Dynamic Sampling via Online Sample-Level Difficulty Estimation for Multimodal RL](https://mlsanity.com/paper/2511.18902/) (2025)
- [Online Resource Allocation with Stochastic Resource Consumption](https://mlsanity.com/paper/2012.07933/) (2020)
- [Online Semi-infinite Linear Programming: Efficient Algorithms via Function Approximation](https://mlsanity.com/paper/2603.16200/) (2026)

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

- [PAIR: Pairwise-Aware Inclusion Reweighting for Adaptive Rollout Allocation in RLVR](https://mlsanity.com/paper/2608.11368/) (2026)
- [SERA: Scale-Equalized Rollout Allocation for Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2609.36552/) (2026)

## Abstract (arXiv)

LLM post-training often relies on reinforcement learning methods that sample multiple rollouts per prompt, yet most existing approaches use a fixed rollout budget for every prompt, despite large differences in the training signal different prompts provide. In this paper, we study adaptive rollout allocation under a fixed global budget and formulate the problem as online resource allocation with prompt-level diminishing returns. Our method, CERO, maintains a Beta posterior over each prompt's success probability and uses the posterior expected Bernoulli variance as a Bayesian estimate of the value of additional rollouts. We use this estimate to construct a concave, saturating utility over cumulative allocations, yielding an objective in which decisions across prompts and epochs are coupled by the global budget. Since the resulting objective is temporally nonseparable, we derive a Fenchel-dual reformulation and update both prompt-level and budget-level dual variables via projected online gradient descent. Under fixed prompt utilities, we prove an O(√K) regret bound against the offline allocation benchmark. Experiments on mathematical-reasoning problems show that CERO consistently outperforms GRPO across multiple open-weight LLMs and benchmarks, demonstrating that adaptive rollout budgeting can improve sample efficiency.