# Thresholding Bandits with Augmented UCB

## TL;DR

This paper introduces AugUCB, an innovative algorithm for thresholding bandits that uses mean and variance estimates to improve arm selection, achieving better practical performance without requiring prior problem complexity knowledge.

## Contribution

The paper presents AugUCB, the first algorithm for TBP that employs both mean and variance estimates for arm elimination, avoiding the need for problem complexity inputs.

## Key findings

- AugUCB outperforms state-of-the-art algorithms like APT and CSAR in simulations.
- AugUCB provides a theoretical upper bound on misclassification probability.
- The algorithm is practical as it does not require prior knowledge of problem complexity.

## Abstract

In this paper we propose the Augmented-UCB (AugUCB) algorithm for a fixed-budget version of the thresholding bandit problem (TBP), where the objective is to identify a set of arms whose quality is above a threshold. A key feature of AugUCB is that it uses both mean and variance estimates to eliminate arms that have been sufficiently explored; to the best of our knowledge this is the first algorithm to employ such an approach for the considered TBP. Theoretically, we obtain an upper bound on the loss (probability of mis-classification) incurred by AugUCB. Although UCBEV in literature provides a better guarantee, it is important to emphasize that UCBEV has access to problem complexity (whose computation requires arms' mean and variances), and hence is not realistic in practice; this is in contrast to AugUCB whose implementation does not require any such complexity inputs. We conduct extensive simulation experiments to validate the performance of AugUCB. Through our simulation work, we establish that AugUCB, owing to its utilization of variance estimates, performs significantly better than the state-of-the-art APT, CSAR and other non variance-based algorithms.