Learning in Markovian bandits with non-observable states and constrained decision epochs
This paper studies regret minimization in Markovian bandits with non-observable states and constrained decision epochs. It introduces self-degrading Markovian bandits, proves that without prior knowledge, algorithms that switch arms rarely suffer super-logarithmic regret, and designs UCB-NOM which achieves nearly logarithmic regret, or O(log T) with prior knowledge.
[2606.27448] Learning in Markovian bandits with non-observable states and constrained decision epochs
[Submitted on 25 Jun 2026]
Title:Learning in Markovian bandits with non-observable states and constrained decision epochs
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Abstract:This paper studies the problem of regret minimization in Markovian bandits with \emph{non-observable states} and possibly \emph{constrained} decision epochs. The focus is restricted to a ``pure'' regret benchmark, that compares the performance of the learning algorithm to the best \emph{pure policy} which -- akin to optimal policies of stochastic bandits -- picks the optimal arm from start to finish without ever switching. We introduce a generalization of rested Markovian bandits, \emph{self-degrading Markovian bandits}, for which pure policies are always asymptotically this http URL show that without prior knowledge on the underlying bandit, the regret of algorithms that switch arms rarely necessarily scales super-logarithmically for every bandit, i.e., as $\omega(\log(T))$, where $T$ is the learning horizon. Despite the unreachability of the logarithmic regime, we design UCB-NOM, an optimistic algorithm inspired by UCB, of which the regret is nearly logarithmic. Lastly, we show that given prior knowledge on the Markovian bandit in the form of a bound on the bias functions of its arm, a proper instantiation of UCB-NOM achieves $O(\log(T))$ regret. We further show that this prior knowledge allows for a $O(\sqrt{T \log(T)})$ worst-case regret bound for UCB-NOM. Notably, our regret bounds do not depend on the number of states of the underlying Markov chains. Our findings suggest that the non-observability of states is a mild inconvenience in self-degrading Markovian bandits.
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2606.27448 [cs.LG]
(or arXiv:2606.27448v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.27448
arXiv-issued DOI via DataCite
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From: Thomas Hira [view email] [v1] Thu, 25 Jun 2026 18:18:15 UTC (754 KB)
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