Low-Rank Bandit Methods for High-Dimensional Dynamic Pricing
This addresses scalable dynamic pricing for e-commerce/retail with many products, though it's incremental within low-rank bandit methods.
The paper tackles dynamic pricing with many products by assuming low-rank structure in demand cross-elasticities, showing this reduces to bandit convex optimization with side information. Their algorithm achieves revenue approaching the best fixed price vector at a rate depending only on intrinsic rank, not product count.
We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimization with side information given by the observed demands. We design dynamic pricing algorithms whose revenue approaches that of the best fixed price vector in hindsight, at a rate that only depends on the intrinsic rank of the demand model and not the number of products. Our approach applies a bandit convex optimization algorithm in a projected low-dimensional space spanned by the latent product features, while simultaneously learning this span via online singular value decomposition of a carefully-crafted matrix containing the observed demands.