Bongsoo Yi

Bongsoo Yi, Yue Kang, Yao Li

The dueling bandit problem, an essential variation of the traditional multi-armed bandit problem, has become significantly prominent recently due to its broad applications in online advertising, recommendation systems, information retrieval, and more. However, in many real-world applications, the feedback for actions is often subject to unavoidable delays and is not immediately available to the agent. This partially observable issue poses a significant challenge to existing dueling bandit literature, as it significantly affects how quickly and accurately the agent can update their policy on the fly. In this paper, we introduce and examine the biased dueling bandit problem with stochastic delayed feedback, revealing that this new practical problem will delve into a more realistic and intriguing scenario involving a preference bias between the selections. We present two algorithms designed to handle situations involving delay. Our first algorithm, requiring complete delay distribution information, achieves the optimal regret bound for the dueling bandit problem when there is no delay. The second algorithm is tailored for situations where the distribution is unknown, but only the expected value of delay is available. We provide a comprehensive regret analysis for the two proposed algorithms and then evaluate their empirical performance on both synthetic and real datasets.

Bongsoo Yi, Yue Kang, Yao Li

The Lipschitz bandit is a key variant of stochastic bandit problems where the expected reward function satisfies a Lipschitz condition with respect to an arm metric space. With its wide-ranging practical applications, various Lipschitz bandit algorithms have been developed, achieving the cumulative regret lower bound of order $\tilde O(T^{(d_z+1)/(d_z+2)})$ over time horizon $T$. Motivated by recent advancements in quantum computing and the demonstrated success of quantum Monte Carlo in simpler bandit settings, we introduce the first quantum Lipschitz bandit algorithms to address the challenges of continuous action spaces and non-linear reward functions. Specifically, we first leverage the elimination-based framework to propose an efficient quantum Lipschitz bandit algorithm named Q-LAE. Next, we present novel modifications to the classical Zooming algorithm, which results in a simple quantum Lipschitz bandit method, Q-Zooming. Both algorithms exploit the computational power of quantum methods to achieve an improved regret bound of $\tilde O(T^{d_z/(d_z+1)})$. Comprehensive experiments further validate our improved theoretical findings, demonstrating superior empirical performance compared to existing Lipschitz bandit methods.