# Online Dynamic Pricing of Complementary Products

arXiv: https://arxiv.org/abs/2511.22291 · HTML: https://mlsanity.com/paper/2511.22291/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 27 Nov 2025.

## Builds on (most cited first, 12 of 12)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Exploiting Similarities among Languages for Machine Translation](https://mlsanity.com/paper/1309.4168/) (2013)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Inferring Networks of Substitutable and Complementary Products](https://mlsanity.com/paper/1506.08839/) (2015)
- [Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1706.00090/) (2017)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Product Knowledge Graph Embedding for E-commerce](https://mlsanity.com/paper/1911.12481/) (2019)
- [Multi-Product Dynamic Pricing in High-Dimensions with Heterogeneous Price Sensitivity](https://mlsanity.com/paper/1901.01030/) (2019)
- [Dynamic Pricing for Airline Ancillaries with Customer Context](https://mlsanity.com/paper/1902.02236/) (2019)
- [Open Problem: Tight Bounds for Kernelized Multi-Armed Bandits with Bernoulli Rewards](https://mlsanity.com/paper/2407.06321/) (2024)
- [Dynamic Pricing with Volume Discounts in Online Settings](https://mlsanity.com/paper/2211.09612/) (2022)
- [A Primal-Dual Online Learning Approach for Dynamic Pricing of Sequentially Displayed Complementary Items under Sale Constraints](https://mlsanity.com/paper/2407.05793/) (2024)

## Abstract (arXiv)

Traditional pricing paradigms, once dominated by static models and rule-based heuristics, are increasingly being replaced by dynamic, data-driven approaches powered by machine learning algorithms. Despite their growing sophistication, most dynamic pricing algorithms focus on optimizing the price of each product independently, disregarding potential interactions among items. By neglecting these interdependencies in consumer demand across related goods, sellers may fail to capture the full potential of coordinated pricing strategies. In this paper, we address this problem by exploring dynamic pricing mechanisms designed explicitly for complementary products, aiming to exploit their joint demand structure to maximize overall revenue. We present an online learning algorithm considering both positive and negative interactions between products' demands. The algorithm utilizes transaction data to identify advantageous complementary relationships through an integer programming problem between different items, and then optimizes pricing strategies using data-driven and computationally efficient multi-armed bandit solutions based on heteroscedastic Gaussian processes. We validate our solution in a simulated environment, and we demonstrate that our solution improves the revenue w.r.t. a comparable learning algorithm ignoring such interactions.