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 $\tilde{\mathcal{O}}\bigl((dK^{-1}+s_{0})\log T\bigr)$. For nonlinear demand residing in a reproducing kernel Hilbert space with effective dimension $\alpha$, complexity $\beta$ and task-similarity parameter $H$, the regret becomes $\tilde{\mathcal{O}}\bigl(K^{-2\alpha\beta/(2\alpha\beta+1)}T^{1/(2\alpha\beta+1)} + H^{2/(2\alpha+1)}T^{1/(2\alpha+1)}\bigr)$, 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*.