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 $\tilde{O}((d\ast K^{-1}+s_0)\log T)$. For nonlinear demand residing in a reproducing kernel Hilbert space with effective dimension $\alpha$, complexity $\beta$ and task-similarity parameter $H$, the regret becomes $\tilde{O}\text{\hspace{0.17em}⁣}(K^{-2\alpha \beta \mathrm{/}(2\alpha \beta +1)}{T}^{1\mathrm{/}(2\alpha \beta +1)}+H^{2\mathrm{/}(2\alpha +1)}{T}^{1\mathrm{/}(2\alpha +1)})$, 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 50% lower cumulative regret and 5 times faster learning 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.