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This paper introduces CURE-UCB, a novel algorithm for Rising Multi-Armed Bandits that leverages knowledge of the time horizon to significantly reduce regret compared to standard approaches. Theoretically, it demonstrates constant regret ($O(1)$) in specific instances where naive methods suffer linear regret growth, and empirical results confirm its superiority across synthetic benchmarks and real-world model selection tasks. This work advances the theoretical understanding of sequential decision-making under non-stationary reward structures.
Rising Multi-Armed Bandits with Known Horizons
arXiv:2602.10727v3 Announce Type: replace Abstract: Rising Multi-Armed Bandits (RMABs) model sequential decision problems where each arm's expected reward improves with repeated pulls. In such problems, the value of investing in an arm depends on how much time remains, making knowledge of the horizon useful side information, yet its benefit remains underexplored. We investigate this benefit through CURE-UCB, a horizon-aware algorithm that estimates each arm's cumulative reward over the remaining horizon. Theoretically, under structured assumptions, we prove that CURE-UCB uniformly dominates a representative horizon-agnostic algorithm and show that the advantage of horizon awareness can be substantial: on some instances, CURE-UCB incurs only $O(1)$ regret whereas the horizon-agnostic algorithm suffers $\Omega(T)$. Furthermore, we establish a regret upper bound for the general concave rising bandit setting whose growth-dependent term matches the known lower bound in its dependence on $T$. Empirically, across synthetic benchmarks and real-world model selection tasks, CURE-UCB achieves lower regret than both rising and non-stationary baselines over a wide range of horizons.
Abstract:Rising Multi-Armed Bandits (RMABs) model sequential decision problems where each arm's expected reward improves with repeated pulls. In such problems, the value of investing in an arm depends on how much time remains, making knowledge of the horizon useful side information, yet its benefit remains underexplored. We investigate this benefit through CURE-UCB, a horizon-aware algorithm that estimates each arm's cumulative reward over the remaining horizon. Theoretically, under structured assumptions, we prove that CURE-UCB uniformly dominates a representative horizon-agnostic algorithm and show that the advantage of horizon awareness can be substantial: on some instances, CURE-UCB incurs only $O(1)$ regret whereas the horizon-agnostic algorithm suffers $\Omega(T)$. Furthermore, we establish a regret upper bound for the general concave rising bandit setting whose growth-dependent term matches the known lower bound in its dependence on $T$. Empirically, across synthetic benchmarks and real-world model selection tasks, CURE-UCB achieves lower regret than both rising and non-stationary baselines over a wide range of horizons.
Machine Learning (cs.LG)
arXiv:2602.10727 [cs.LG]
(or arXiv:2602.10727v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2602.10727 Focus to learn more arXiv-issued DOI via DataCite
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