Meta Dynamic Pricing: Learning Across Experiments
50 Pages Posted: 6 Mar 2019 Last revised: 8 May 2019
Date Written: February 14, 2019
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 prior as a function of its estimation error, thereby ensuring convergence of each price experiment. 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 or a naive approach of greedily using the updated prior across products.
Keywords: Thompson sampling, transfer learning, dynamic pricing, meta learning
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