Exploration, Exploitation, and Engagement in Multi-Armed Bandits with Abandonment

TL;DR

This paper introduces a new multi-armed bandit model incorporating user abandonment based on engagement, proposing algorithms with proven logarithmic regret and demonstrating superior performance over traditional methods.

Contribution

The paper develops the MAB-A model accounting for user abandonment and proposes ULCB and KL-ULCB algorithms with theoretical regret bounds and practical improvements.

Findings

Both algorithms achieve $O( ext{log} K)$ regret.

KL-ULCB's regret bound is asymptotically sharp.

Algorithms outperform traditional UCB, KL-UCB, and Q-learning in simulations.

Abstract

Multi-armed bandit (MAB) is a classic model for understanding the exploration-exploitation trade-off. The traditional MAB model for recommendation systems assumes the user stays in the system for the entire learning horizon. In new online education platforms such as ALEKS or new video recommendation systems such as TikTok and YouTube Shorts, the amount of time a user spends on the app depends on how engaging the recommended contents are. Users may temporarily leave the system if the recommended items cannot engage the users. To understand the exploration, exploitation, and engagement in these systems, we propose a new model, called MAB-A where "A" stands for abandonment and the abandonment probability depends on the current recommended item and the user's past experience (called state). We propose two algorithms, ULCB and KL-ULCB, both of which do more exploration (being optimistic) when the user likes the previous recommended item and less exploration (being pessimistic) when the user does not like the previous item. We prove that both ULCB and KL-ULCB achieve logarithmic regret, $O(\log K)$, where $K$ is the number of visits (or episodes). Furthermore, the regret bound under KL-ULCB is asymptotically sharp. We also extend the proposed algorithms to the general-state setting. Simulation results confirm our theoretical analysis and show that the proposed algorithms have significantly lower regrets than the traditional UCB and KL-UCB, and Q-learning-based algorithms.