Meta Dynamic Pricing : Transfer Learning Across Experiments

We study the problem of learning shared structure 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 (meta-exploration) with the need to leverage the estimated prior to achieve good performance (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; an immediate consequence of our analysis is that the price of an unknown prior in Thompson sampling is negligible in experiment-rich environments with shared structure (large N). Numerical experiments on synthetic and real auto loan data demonstrate that our algorithm significantly speeds up learning compared to prior-independent algorithms