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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.15073 |
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| _version_ | 1866915501385449472 |
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| author | Li, Shaoang Li, Jian |
| author_facet | Li, Shaoang Li, Jian |
| contents | Non-stationary multi-armed bandits enable agents to adapt to changing environments by incorporating mechanisms to detect and respond to shifts in reward distributions, making them well-suited for dynamic settings. However, existing approaches typically assume that reward feedback is available at every round - an assumption that overlooks many real-world scenarios where feedback is limited. In this paper, we take a significant step forward by introducing a new model of constrained feedback in non-stationary multi-armed bandits, where the availability of reward feedback is restricted. We propose the first prior-free algorithm - that is, one that does not require prior knowledge of the degree of non-stationarity - that achieves near-optimal dynamic regret in this setting. Specifically, our algorithm attains a dynamic regret of $\tilde{\mathcal{O}}({K^{1/3} V_T^{1/3} T }/{ B^{1/3}})$, where $T$ is the number of rounds, $K$ is the number of arms, $B$ is the query budget, and $V_T$ is the variation budget capturing the degree of non-stationarity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constrained Feedback Learning for Non-Stationary Multi-Armed Bandits Li, Shaoang Li, Jian Machine Learning Non-stationary multi-armed bandits enable agents to adapt to changing environments by incorporating mechanisms to detect and respond to shifts in reward distributions, making them well-suited for dynamic settings. However, existing approaches typically assume that reward feedback is available at every round - an assumption that overlooks many real-world scenarios where feedback is limited. In this paper, we take a significant step forward by introducing a new model of constrained feedback in non-stationary multi-armed bandits, where the availability of reward feedback is restricted. We propose the first prior-free algorithm - that is, one that does not require prior knowledge of the degree of non-stationarity - that achieves near-optimal dynamic regret in this setting. Specifically, our algorithm attains a dynamic regret of $\tilde{\mathcal{O}}({K^{1/3} V_T^{1/3} T }/{ B^{1/3}})$, where $T$ is the number of rounds, $K$ is the number of arms, $B$ is the query budget, and $V_T$ is the variation budget capturing the degree of non-stationarity. |
| title | Constrained Feedback Learning for Non-Stationary Multi-Armed Bandits |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.15073 |