Transfer Learning for Contextual Joint Assortment-Pricing under Cross-Market Heterogeneity

We study dynamic joint assortment and pricing where a seller updates decisions at regular accounting/operating intervals to maximize the cumulative per-period revenue over a horizon $T$. In many settings, assortment and prices affect not only what an arriving customer buys but also how many customers arrive within the period, whereas classical multinomial logit (MNL) models assume arrivals as fixed, potentially leading to suboptimal decisions. We propose a Poisson-MNL model that couples a contextual MNL choice model with a Poisson arrival model whose rate depends on the offered assortment and prices. Building on this model, we develop an efficient algorithm PMNL based on the idea of upper confidence bound (UCB). We establish its (near) optimality by proving a non-asymptotic regret bound of order $\sqrt{T\log{T}}$ and a matching lower bound (up to $\log T$). Simulation studies underscore the importance of accounting for the dependency of arrival rates on assortment and pricing: PMNL effectively learns customer choice and arrival models and provides joint assortment-pricing decisions that outperform others that assume fixed arrival rates.

Many consumer decisions are repeated choices under uncertainty. Standard models capture these decisions using Bayesian learning and dynamic programming: consumers update beliefs from feedback and use those beliefs to guide future choices. In many markets, however, learning does not restart when consumers enter a new context: prior experience with a brand, product, or provider can shape beliefs in later, related decisions. We study this cross-context knowledge transfer, or meta-learning, in sequential choice. We design a hierarchical laboratory task in which participants repeatedly choose among airlines across routes and observe noisy binary outcomes. Reduced-form evidence shows that participants improve not only within routes, but also across routes: they choose better airlines earlier in later routes and reduce pseudo-regret. To identify the mechanism behind this transfer, we compare human choices to a no-transfer benchmark and a fully integrated Bayesian meta-learning benchmark. In particular, we introduce a class of boundedly rational meta dynamic programming policies, BRMDP(D), that approximate full integration using a limited number of hyper-posterior draws, denoted by D. Trial-by-trial likelihood comparisons show that low-D boundedly rational meta-learning, especially BRMDP(1), fits participant behavior better than both no transfer and fully integrated Bayesian transfer. Consumers, therefore, transfer brand-level regularities across contexts, but through coarse representations of prior uncertainty. The findings imply that models of consumer learning should allow for approximate cross-context transfer, and that managerial counterfactuals based on either no-transfer or fully integrated learning can be misleading.

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.