# Dynamic Pricing and Demand Learning on a Large Network of Products: A PAC-Bayesian Approach

arXiv: https://arxiv.org/abs/2111.00790 · HTML: https://mlsanity.com/paper/2111.00790/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 6 of 6)

- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020)
- [Approximation beats concentration? An approximation view on inference with smooth radial kernels](https://mlsanity.com/paper/1801.03437/) (2018)
- [Online learning with kernel losses](https://mlsanity.com/paper/1802.09732/) (2018)
- [Small Sample Spaces for Gaussian Processes](https://mlsanity.com/paper/2103.03169/) (2021)

## Built on by (most cited first, 1 of 1)

- [A Reinforcement Learning Approach in Multi-Phase Second-Price Auction Design](https://mlsanity.com/paper/2210.10278/) (2022)

## Abstract (arXiv)

We consider a seller offering a large network of N products over a time horizon of T periods. The seller does not know the parameters of the products' linear demand model, and can dynamically adjust product prices to learn the demand model based on sales observations. The seller aims to minimize its pseudo-regret, i.e., the expected revenue loss relative to a clairvoyant who knows the underlying demand model. We consider a sparse set of demand relationships between products to characterize various connectivity properties of the product network. In particular, we study three different sparsity frameworks: (1) L0 sparsity, which constrains the number of connections in the network, and (2) off-diagonal sparsity, which constrains the magnitude of cross-product price sensitivities, and (3) a new notion of spectral sparsity, which constrains the asymptotic decay of a similarity metric on network nodes. We propose a dynamic pricing-and-learning policy that combines the optimism-in-the-face-of-uncertainty and PAC-Bayesian approaches, and show that this policy achieves asymptotically optimal performance in terms of N and T. We also show that in the case of spectral and off-diagonal sparsity, the seller can have a pseudo-regret linear in N, even when the network is dense.