# An Asymptotically Optimal Strategy for Constrained Multi-armed Bandit Problems

arXiv: https://arxiv.org/abs/1805.01237 · HTML: https://mlsanity.com/paper/1805.01237/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2018.

## Built on by (most cited first, 3 of 3)

- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [Constrained Pure Exploration Multi-Armed Bandits with a Fixed Budget](https://mlsanity.com/paper/2211.14768/) (2022)
- [Multi-Metric Adaptive Experimental Design Under a Fixed Budget with Validation](https://mlsanity.com/paper/2506.03062/) (2025)

## Abstract (arXiv)

For the stochastic multi-armed bandit (MAB) problem from a constrained model that generalizes the classical one, we show that an asymptotic optimality is achievable by a simple strategy extended from the εt-greedy strategy. We provide a finite-time lower bound on the probability of correct selection of an optimal near-feasible arm that holds for all time steps. Under some conditions, the bound approaches one as time t goes to infinity. A particular example sequence of εt having the asymptotic convergence rate in the order of (1-frac1t)4 that holds from a sufficiently large t is also discussed.