Transfer Learning for Contextual Joint Assortment-Pricing under Cross-Market Heterogeneity
This work addresses a domain-specific problem in e-commerce and retail for sellers needing efficient pricing strategies across diverse markets, representing an incremental advance by adapting existing transfer learning and bandit methods to a structured utility model.
The paper tackles the problem of accelerating learning in joint assortment-pricing across multiple markets with heterogeneous customer preferences, achieving regret bounds that show transfer learning reduces variance but incurs an irreducible bias cost, with numerical experiments confirming TJAP outperforms baseline methods.
We study transfer learning for contextual joint assortment-pricing under a multinomial logit choice model with bandit feedback. A seller operates across multiple related markets and observes only posted prices and realized purchases. While data from source markets can accelerate learning in a target market, cross-market differences in customer preferences may introduce systematic bias if pooled indiscriminately. We model heterogeneity through a structured utility shift, where markets share a common contextual utility structure but differ along a sparse set of latent preference coordinates. Building on this, we develop Transfer Joint Assortment-Pricing (TJAP), a bias-aware framework that combines aggregate-then-debias estimation with a UCB-style policy. TJAP constructs two-radius confidence bounds that separately capture statistical uncertainty and transfer-induced bias, uniformly over continuous prices. We establish matching minimax regret bounds of order $\tilde{O}\!\left(d\sqrt{\frac{T}{1+H}} + s_0\sqrt{T}\right),$revealing a transparent variance-bias tradeoff: transfer accelerates learning along shared preference directions, while heterogeneous components impose an irreducible adaptation cost. Numerical experiments corroborate the theory, showing that TJAP outperforms both target-only learning and naive pooling while remaining robust to cross-market differences.