Title:	Best arm in Continuous Bandits and Variational Quantum Algorithms
DNr:	NAISS 2025/22-47
Project Type:	NAISS Small Compute
Principal Investigator:	Marc Constantin Wanner <wanner@chalmers.se>
Affiliation:	Chalmers tekniska högskola
Duration:	2025-01-21 – 2025-04-01
Classification:	10201
Keywords:

Abstract

We study pure exploration for stochastic ban- dits where the set of arms is given by the d- dimensional unit-cube and the expected payoff is Lipschitz. While regret minimization has been ad- dressed in this setting, existing methods for pure exploration only cover discrete payoff. We initi- ate the study of pure exploration in a continuous setting. We derive a fixed-confidence information- theoretic lower bound. Under certain assumptions on the expected payoff, we show that this bound can be discretely approximated from below and derive a simple algorithm, which is near-optimal with respect to an instance specific lower bound. Finally, we present numerical experiments that validate our theoretical bounds and provide a com- parison of our algorithm’s performance with that of other existing algorithms.