Meta Dynamic Pricing: Transfer Learning Across Experiments

TL;DR

This paper introduces a meta learning approach for dynamic pricing across multiple related products, efficiently learning shared demand structures to improve pricing strategies and reduce regret in experiment-rich environments.

Contribution

It proposes a novel meta dynamic pricing algorithm that learns a shared prior online, balancing exploration and exploitation, with a new prior alignment technique for analyzing regret with mis-specified priors.

Findings

Meta regret grows sublinearly with number of products N.

Algorithm significantly speeds up learning compared to prior-independent methods.

Demonstrated effectiveness on synthetic and real auto loan data.

Abstract

We study the problem of learning shared structure \emph{across} a sequence of dynamic pricing experiments for related products. We consider a practical formulation where the unknown demand parameters for each product come from an unknown distribution (prior) that is shared across products. We then propose a meta dynamic pricing algorithm that learns this prior online while solving a sequence of Thompson sampling pricing experiments (each with horizon $T$) for $N$ different products. Our algorithm addresses two challenges: (i) balancing the need to learn the prior (\emph{meta-exploration}) with the need to leverage the estimated prior to achieve good performance (\emph{meta-exploitation}), and (ii) accounting for uncertainty in the estimated prior by appropriately "widening" the estimated prior as a function of its estimation error. We introduce a novel prior alignment technique to analyze the regret of Thompson sampling with a mis-specified prior, which may be of independent interest. Unlike prior-independent approaches, our algorithm's meta regret grows sublinearly in $N$, demonstrating that the price of an unknown prior in Thompson sampling can be negligible in experiment-rich environments (large $N$). Numerical experiments on synthetic and real auto loan data demonstrate that our algorithm significantly speeds up learning compared to prior-independent algorithms.