Non-Stationary Online Resource Allocation: Learning from a Single Sample
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arXiv
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| Format: | Preprint |
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2026
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| author | Feng, Yiding Jiang, Jiashuo Wang, Yige |
| author_facet | Feng, Yiding Jiang, Jiashuo Wang, Yige |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18114 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Stationary Online Resource Allocation: Learning from a Single Sample Feng, Yiding Jiang, Jiashuo Wang, Yige Machine Learning Data Structures and Algorithms Optimization and Control 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. |
| title | Non-Stationary Online Resource Allocation: Learning from a Single Sample |
| topic | Machine Learning Data Structures and Algorithms Optimization and Control |
| url | https://arxiv.org/abs/2602.18114 |