Transfer Faster, Price Smarter: Minimax Dynamic Pricing under Cross-Market Preference Shift

We study contextual dynamic pricing when a target market can leverage $K$ auxiliary markets—offline logs or concurrent streams—whose mean utilities differ by a structured preference shift. We propose Cross-Market Transfer Dynamic Pricing (CM-TDP), the first algorithm that provably handles such model-shift transfer and delivers minimax-optimal regret for both linear and non-parametric utility models.

For linear utilities of dimension $d$, where the difference between source- and target-task coefficients is $s_0$-sparse, CM-TDP attains regret $\tilde{\mathcal{O}}((d{K}^{-1}+s_0)\log T)$. For nonlinear demand residing in a reproducing kernel Hilbert space with effective dimension $\alpha$, complexity $\beta$ and task-similarity parameter $H$, the regret becomes $\tilde{\mathcal{O}}(K^{-2\alpha \beta /(2\alpha \beta +1)}{T}^{1/(2\alpha \beta +1)}+H^{2/(2\alpha +1)}{T}^{1/(2\alpha +1)})$, matching information-theoretic lower bounds up to logarithmic factors. The RKHS bound is the first of its kind for transfer pricing and is of independent interest.

Extensive simulations show up to 38% higher cumulative revenue and $6\times$ faster convergence relative to single-market pricing baselines. By bridging transfer learning, robust aggregation, and revenue optimization, CM-TDP moves toward pricing systems that transfer faster, price smarter.