Recommender systems play a crucial role in internet economies by connecting
users with relevant products or services. However, designing effective
recommender systems faces two key challenges: (1) the exploration-exploitation
tradeoff in balancing new product exploration against exploiting known
preferences, and (2) dynamic incentive compatibility in accounting for users'
self-interested behaviors and heterogeneous preferences. This paper formalizes
these challenges into a Dynamic Bayesian Incentive-Compatible Recommendation
Protocol (DBICRP). To address the DBICRP, we propose a two-stage algorithm
(RCB) that integrates incentivized exploration with an efficient offline
learning component for exploitation. In the first stage, our algorithm explores
available products while maintaining dynamic incentive compatibility to
determine sufficient sample sizes. The second stage employs inverse
proportional gap sampling integrated with an arbitrary machine learning method
to ensure sublinear regret. Theoretically, we prove that RCB achieves
$O(\sqrt{KdT})$ regret and satisfies Bayesian incentive compatibility (BIC)
under a Gaussian prior assumption. Empirically, we validate RCB's strong
incentive gain, sublinear regret, and robustness through simulations and a
real-world application on personalized warfarin dosing. Our work provides a
principled approach for incentive-aware recommendation in online preference
learning settings.

推荐系统在互联网经济中起着至关重要的作用，本论文提出了一种 Dynamic Bayesian Incentive-Compatible Recommendation Protocol (DBICRP) 来解决有效设计推荐系统所面临的挑战，同时还提出了一种基于两阶段算法 (RCB) 的方法来集成激励探索和高效的离线学习，以达到亚线性遗憾和贝叶斯激励兼容。在理论上，证明了 RCB 算法在高斯先验假设下实现了 O (sqrt (KdT)) 的遗憾和贝叶斯激励兼容，实证上通过模拟和实际应用验证了 RCB 算法的强激励增益、亚线性遗憾和鲁棒性，从而为在线偏好学习中的激励感知推荐提供了一个有原则的方法。