Non-Stationary Latent Auto-Regressive Bandits
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917939735691264 |
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| author | Trella, Anna L. Dempsey, Walter Gazi, Asim H. Xu, Ziping Doshi-Velez, Finale Murphy, Susan A. |
| author_facet | Trella, Anna L. Dempsey, Walter Gazi, Asim H. Xu, Ziping Doshi-Velez, Finale Murphy, Susan A. |
| contents | For the non-stationary multi-armed bandit (MAB) problem, many existing methods allow a general mechanism for the non-stationarity, but rely on a budget for the non-stationarity that is sub-linear to the total number of time steps $T$. In many real-world settings, however, the mechanism for the non-stationarity can be modeled, but there is no budget for the non-stationarity. We instead consider the non-stationary bandit problem where the reward means change due to a latent, auto-regressive (AR) state. We develop Latent AR LinUCB (LARL), an online linear contextual bandit algorithm that does not rely on the non-stationary budget, but instead forms good predictions of reward means by implicitly predicting the latent state. The key idea is to reduce the problem to a linear dynamical system which can be solved as a linear contextual bandit. In fact, LARL approximates a steady-state Kalman filter and efficiently learns system parameters online. We provide an interpretable regret bound for LARL with respect to the level of non-stationarity in the environment. LARL achieves sub-linear regret in this setting if the noise variance of the latent state process is sufficiently small with respect to $T$. Empirically, LARL outperforms various baseline methods in this non-stationary bandit problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Stationary Latent Auto-Regressive Bandits Trella, Anna L. Dempsey, Walter Gazi, Asim H. Xu, Ziping Doshi-Velez, Finale Murphy, Susan A. Machine Learning Artificial Intelligence For the non-stationary multi-armed bandit (MAB) problem, many existing methods allow a general mechanism for the non-stationarity, but rely on a budget for the non-stationarity that is sub-linear to the total number of time steps $T$. In many real-world settings, however, the mechanism for the non-stationarity can be modeled, but there is no budget for the non-stationarity. We instead consider the non-stationary bandit problem where the reward means change due to a latent, auto-regressive (AR) state. We develop Latent AR LinUCB (LARL), an online linear contextual bandit algorithm that does not rely on the non-stationary budget, but instead forms good predictions of reward means by implicitly predicting the latent state. The key idea is to reduce the problem to a linear dynamical system which can be solved as a linear contextual bandit. In fact, LARL approximates a steady-state Kalman filter and efficiently learns system parameters online. We provide an interpretable regret bound for LARL with respect to the level of non-stationarity in the environment. LARL achieves sub-linear regret in this setting if the noise variance of the latent state process is sufficiently small with respect to $T$. Empirically, LARL outperforms various baseline methods in this non-stationary bandit problem. |
| title | Non-Stationary Latent Auto-Regressive Bandits |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2402.03110 |