# Rising Rested Bandits: Lower Bounds and Efficient Algorithms

arXiv: https://arxiv.org/abs/2411.14446 · HTML: https://mlsanity.com/paper/2411.14446/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 45 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Builds on (most cited first, 5 of 5)

- [Regret Bound Balancing and Elimination for Model Selection in Bandits and RL](https://mlsanity.com/paper/2012.13045/) (2020)
- [Regret Balancing for Bandit and RL Model Selection](https://mlsanity.com/paper/2006.05491/) (2020)
- [Sliding-Window Thompson Sampling for Non-Stationary Settings](https://mlsanity.com/paper/2409.05181/) (2024)
- [Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits](https://mlsanity.com/paper/1902.01575/) (2019)
- [Linear Bandits with Memory: from Rotting to Rising](https://mlsanity.com/paper/2302.08345/) (2023)

## Built on by (most cited first, 2 of 2)

- [Combinatorial Rising Bandits](https://mlsanity.com/paper/2412.00798/) (2024)
- [Rising Multi-Armed Bandits with Known Horizons](https://mlsanity.com/paper/2602.10727/) (2026)

## Abstract (arXiv)

This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e. those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. arm). We study a particular case of the rested bandits in which the arms' expected reward is monotonically non-decreasing and concave. We study the inherent sample complexity of the regret minimization problem by deriving suitable regret lower bounds. Then, we design an algorithm for the rested case textitR-ed-UCB, providing a regret bound depending on the properties of the instance and, under certain circumstances, of widetildeO(T^frac23). We empirically compare our algorithms with state-of-the-art methods for non-stationary MABs over several synthetically generated tasks and an online model selection problem for a real-world dataset