# Upper Confidence Bounds for Combining Stochastic Bandits

arXiv: https://arxiv.org/abs/2012.13115 · HTML: https://mlsanity.com/paper/2012.13115/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2020.

## Built on by (most cited first, 7 of 7)

- [The Pareto Frontier of model selection for general Contextual Bandits](https://mlsanity.com/paper/2110.13282/) (2021)
- [Pareto Optimal Model Selection in Linear Bandits](https://mlsanity.com/paper/2102.06593/) (2021)
- [Offline-to-online hyperparameter transfer for stochastic bandits](https://mlsanity.com/paper/2501.02926/) (2025)
- [Linear Bandits with Memory: from Rotting to Rising](https://mlsanity.com/paper/2302.08345/) (2023)
- [Universal and data-adaptive algorithms for model selection in linear contextual bandits](https://mlsanity.com/paper/2111.04688/) (2021)
- [Causal Bandits: The Pareto Optimal Frontier of Adaptivity, a Reduction to Linear Bandits, and Limitations around Unknown Marginals](https://mlsanity.com/paper/2407.00950/) (2024)
- [Generalized Linear Bandits with Memory](https://mlsanity.com/paper/2608.15848/) (2026)

## Abstract (arXiv)

We provide a simple method to combine stochastic bandit algorithms. Our approach is based on a "meta-UCB" procedure that treats each of N individual bandit algorithms as arms in a higher-level N-armed bandit problem that we solve with a variant of the classic UCB algorithm. Our final regret depends only on the regret of the base algorithm with the best regret in hindsight. This approach provides an easy and intuitive alternative strategy to the CORRAL algorithm for adversarial bandits, without requiring the stability conditions imposed by CORRAL on the base algorithms. Our results match lower bounds in several settings, and we provide empirical validation of our algorithm on misspecified linear bandit and model selection problems.