Nonparametric Self-Adjusting Control for Joint Learning and Optimization of Multiproduct Pricing with Finite Resource Capacity

We study a multiperiod network revenue management problem where a seller sells multiple products made from multiple resources with finite capacity in an environment where the underlying demand function is a priori unknown (in the nonparametric sense). The objective of the seller is to simultaneously learn the unknown demand function and dynamically price the products to minimize the expected revenue loss. For the problem where the number of selling periods and initial capacity are scaled by $k>0$, it is known that the expected revenue loss of any non-anticipating pricing policy is $\mathrm{\Omega }\left(\sqrt{k}\right)$. However, there is a considerable gap between this theoretical lower bound and the performance bound of the best-known heuristic control in the literature. In this paper, we propose a nonparametric self-adjusting control and show that its expected revenue loss is $\mathcal{O}\left(k^{1/2+ϵ}\log k\right)$ for any arbitrarily small $ϵ>0$, provided that the underlying demand function is sufficiently smooth. This is the tightest bound of its kind for the problem setting that we consider in this paper, and it significantly improves the performance bound of existing heuristic controls in the literature. In addition, our intermediate results on the large deviation bounds for spline estimation and nonparametric stability analysis of constrained optimization are of independent interest and are potentially useful for other applications.

The online appendix is available at https://doi.org/10.1287/moor.2018.0937.