# Doubly Fair Dynamic Pricing

arXiv: https://arxiv.org/abs/2209.11837 · HTML: https://mlsanity.com/paper/2209.11837/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 23 Sep 2022.

## Builds on (most cited first, 23 of 23)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Fairness in Machine Learning](https://mlsanity.com/paper/2012.15816/) (2020)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [Online Learning with Switching Costs and Other Adaptive Adversaries](https://mlsanity.com/paper/1302.4387/) (2013)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Private Reinforcement Learning with PAC and Regret Guarantees](https://mlsanity.com/paper/2009.09052/) (2020)
- [Individual Fairness in Hindsight](https://mlsanity.com/paper/1812.04069/) (2018)
- [Decision Making with Differential Privacy under a Fairness Lens](https://mlsanity.com/paper/2105.07513/) (2021)
- [Sample-Efficient Reinforcement Learning with loglog(T) Switching Cost](https://mlsanity.com/paper/2202.06385/) (2022)
- [Metric-Free Individual Fairness in Online Learning](https://mlsanity.com/paper/2002.05474/) (2020)
- [Contextual Search via Intrinsic Volumes](https://mlsanity.com/paper/1804.03195/) (2018)
- [Policy Optimization Using Semi-parametric Models for Dynamic Pricing](https://mlsanity.com/paper/2109.06368/) (2021)
- [Differentially Private Regret Minimization in Episodic Markov Decision Processes](https://mlsanity.com/paper/2112.10599/) (2021)
- [Local Differential Privacy for Regret Minimization in Reinforcement Learning](https://mlsanity.com/paper/2010.07778/) (2020)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (2021)
- [Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise](https://mlsanity.com/paper/2201.11341/) (2022)
- [Offline Reinforcement Learning with Differential Privacy](https://mlsanity.com/paper/2206.00810/) (2022)
- [Provably Confidential Language Modelling](https://mlsanity.com/paper/2205.01863/) (2022)
- [Differentially Private Linear Sketches: Efficient Implementations and Applications](https://mlsanity.com/paper/2205.09873/) (2022)
- [Reinforcement Learning for Fair Dynamic Pricing](https://mlsanity.com/paper/1803.09967/) (2018)
- [Fairness-aware Online Price Discrimination with Nonparametric Demand Models](https://mlsanity.com/paper/2111.08221/) (2021)

## Built on by (most cited first, 8 of 8)

- [Near-Optimal Differentially Private Reinforcement Learning](https://mlsanity.com/paper/2212.04680/) (2022)
- [Stable Minima Cannot Overfit in Univariate ReLU Networks: Generalization by Large Step Sizes](https://mlsanity.com/paper/2406.06838/) (2024)
- [Pricing with Contextual Elasticity and Heteroscedastic Valuation](https://mlsanity.com/paper/2312.15999/) (2023)
- [Utility Fairness in Contextual Dynamic Pricing with Demand Learning](https://mlsanity.com/paper/2311.16528/) (2023)
- [Near-Optimal Reinforcement Learning with Self-Play under Adaptivity Constraints](https://mlsanity.com/paper/2402.01111/) (2024)
- [Online Pricing and Allocation with Demand Learning and Fulfillment Cost](https://mlsanity.com/paper/2501.18049/) (2025)
- [Dynamic Pricing with Adversarially-Censored Demands](https://mlsanity.com/paper/2502.06168/) (2025)
- [Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand](https://mlsanity.com/paper/2605.05609/) (2026)

## Abstract (arXiv)

We study the problem of online dynamic pricing with two types of fairness constraints: a "procedural fairness" which requires the proposed prices to be equal in expectation among different groups, and a "substantive fairness" which requires the accepted prices to be equal in expectation among different groups. A policy that is simultaneously procedural and substantive fair is referred to as "doubly fair". We show that a doubly fair policy must be random to have higher revenue than the best trivial policy that assigns the same price to different groups. In a two-group setting, we propose an online learning algorithm for the 2-group pricing problems that achieves tildeO(√T) regret, zero procedural unfairness and tildeO(√T) substantive unfairness over T rounds of learning. We also prove two lower bounds showing that these results on regret and unfairness are both information-theoretically optimal up to iterated logarithmic factors. To the best of our knowledge, this is the first dynamic pricing algorithm that learns to price while satisfying two fairness constraints at the same time.