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

Abstract

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 $\hat{I}\pm$, complexity ${\hat{I}}^2$ and task-similarity parameter $H$, the regret becomes $\tilde{O}(K^{-2\hat{I}\pm {\hat{I}}^2/(2\hat{I}\pm {\hat{I}}^2+1)}{T}^{1/(2\hat{I}\pm {\hat{I}}^2+1)}+H^{2/(2\hat{I}\pm +1)}{T}^{1/(2\hat{I}\pm +1)})$, 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.