Yige Wang

Yiming Zong, Yige Wang, Jiashuo Jiang

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 $O(\sqrt{K})$ 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.

Yiding Feng, Jiashuo Jiang, Yige Wang

We study online resource allocation under non-stationary demand with a minimum offline data requirement. In this problem, a decision-maker must allocate multiple types of resources to sequentially arriving queries over a finite horizon. Each query belongs to a finite set of types with fixed resource consumption and a stochastic reward drawn from an unknown, type-specific distribution. Critically, the environment exhibits arbitrary non-stationarity -- arrival distributions may shift unpredictably-while the algorithm requires only one historical sample per period to operate effectively. We distinguish two settings based on sample informativeness: (i) reward-observed samples containing both query type and reward realization, and (ii) the more challenging type-only samples revealing only query type information. We propose a novel type-dependent quantile-based meta-policy that decouples the problem into modular components: reward distribution estimation, optimization of target service probabilities via fluid relaxation, and real-time decisions through dynamic acceptance thresholds. For reward-observed samples, our static threshold policy achieves $\tilde{O}(\sqrt{T})$ regret. For type-only samples, we first establish that sublinear regret is impossible without additional structure; under a mild minimum-arrival-probability assumption, we design both a partially adaptive policy attaining the same $\tilde{O}({T})$ bound and, more significantly, a fully adaptive resolving policy with careful rounding that achieves the first poly-logarithmic regret guarantee of $O((\log T)^3)$ for non-stationary multi-resource allocation. Our framework advances prior work by operating with minimal offline data (one sample per period), handling arbitrary non-stationarity without variation-budget assumptions, and supporting multiple resource constraints.