We study the dynamic joint assortment selection and positioning problem, where the attraction of each product depends on both its intrinsic appeal and its display position under a Multinomial Logit (MNL) choice framework. Our study ranges from the multiplicative position effects model, in which each product's attraction is scaled by a position-specific factor, to a general position effects model assigning independent attraction parameters to every product--position pair to capture heterogeneous synergies. For both models, we design round-based learning algorithms that update decisions after every single feedback, and establish the first regret-optimal characterization. Besides, our round-based algorithms provide the prompt operations needed by modern platforms. For the multiplicative model, we develop a cross-position pairwise maximum likelihood estimator with a clipping mechanism, and prove that our algorithm P2MLE-UCB attains a regret of $\tilde{O}(\sqrt{NT})$, matching the lower bound and closing the $\sqrt{K}$ gap left by prior epoch-based analyses. For the general model, we establish a minimax lower bound and propose GP2-UCB with a matching upper bound. Moreover, we design an efficient subroutine for the per-round joint assortment and positioning optimization based on Dinkelbach's method and maximum-weight bipartite matching. Numerical experiments on synthetic data and the Expedia dataset show that our algorithms consistently outperform state-of-the-art benchmarks.

翻译：我们研究了动态联合品类选择与位置优化问题，其中每个产品的吸引力在多项Logit（MNL）选择框架下同时取决于其内在吸引力和展示位置。我们的研究范围从乘法位置效应模型（每个产品的吸引力通过位置特定因子进行缩放）扩展到一般位置效应模型（为每个产品-位置对分配独立吸引力参数以捕捉异质性协同效应）。针对这两种模型，我们设计了基于轮次的学习算法，该算法在每次反馈后更新决策，并首次建立了后悔最优特性刻画。此外，我们的轮次算法为现代平台提供了所需的即时操作。对于乘法模型，我们开发了带裁剪机制的跨位置成对极大似然估计器，并证明算法P2MLE-UCB的后悔值达到$\tilde{O}(\sqrt{NT})$，匹配理论下界且弥合了先前基于阶段分析留下的$\sqrt{K}$差距。对于一般模型，我们建立了极小化极大下界，并提出具有匹配上界的GP2-UCB算法。此外，我们基于Dinkelbach方法与最大权二分匹配设计了每轮联合品类与位置优化的高效子程序。在合成数据集和Expedia数据集上的数值实验表明，我们的算法始终优于现有最优基准方法。