Sequential Decision Problems with Missing Feedback
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912502314434560 |
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| author | Palomba, Filippo |
| author_facet | Palomba, Filippo |
| contents | This paper investigates the challenges of optimal online policy learning under missing data. State-of-the-art algorithms implicitly assume that rewards are always observable. I show that when rewards are missing at random, the Upper Confidence Bound (UCB) algorithm maintains optimal regret bounds; however, it selects suboptimal policies with high probability as soon as this assumption is relaxed. To overcome this limitation, I introduce a fully nonparametric algorithm-Doubly-Robust Upper Confidence Bound (DR-UCB)-which explicitly models the form of missingness through observable covariates and achieves a nearly-optimal worst-case regret rate of $\widetilde{O}(\sqrt{T})$. To prove this result, I derive high-probability bounds for a class of doubly-robust estimators that hold under broad dependence structures. Simulation results closely match the theoretical predictions, validating the proposed framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequential Decision Problems with Missing Feedback Palomba, Filippo Econometrics This paper investigates the challenges of optimal online policy learning under missing data. State-of-the-art algorithms implicitly assume that rewards are always observable. I show that when rewards are missing at random, the Upper Confidence Bound (UCB) algorithm maintains optimal regret bounds; however, it selects suboptimal policies with high probability as soon as this assumption is relaxed. To overcome this limitation, I introduce a fully nonparametric algorithm-Doubly-Robust Upper Confidence Bound (DR-UCB)-which explicitly models the form of missingness through observable covariates and achieves a nearly-optimal worst-case regret rate of $\widetilde{O}(\sqrt{T})$. To prove this result, I derive high-probability bounds for a class of doubly-robust estimators that hold under broad dependence structures. Simulation results closely match the theoretical predictions, validating the proposed framework. |
| title | Sequential Decision Problems with Missing Feedback |
| topic | Econometrics |
| url | https://arxiv.org/abs/2507.19596 |