Multi-Armed Bandits and Quantum Channel Oracles

TL;DR

This paper explores quantum algorithms for multi-armed bandit problems, demonstrating that limited access to reward randomness prevents quantum speed-ups, thus generalizing previous results on unstructured search.

Contribution

It introduces new bandit models with restricted reward access and proves that quantum query complexity matches classical algorithms under these conditions.

Findings

Quantum speed-up is possible with full superposition access to rewards.

Limited reward access negates quantum advantage, matching classical complexity.

Generalizes prior results on unstructured search with probabilistic oracles.

Abstract

Multi-armed bandits are one of the theoretical pillars of reinforcement learning. Recently, the investigation of quantum algorithms for multi-armed bandit problems was started, and it was found that a quadratic speed-up (in query complexity) is possible when the arms and the randomness of the rewards of the arms can be queried in superposition. Here we introduce further bandit models where we only have limited access to the randomness of the rewards, but we can still query the arms in superposition. We show that then the query complexity is the same as for classical algorithms. This generalizes the prior result that no speed-up is possible for unstructured search when the oracle has positive failure probability.