# Convex Surrogate Loss Functions for Contextual Pricing with Transaction Data

arXiv: https://arxiv.org/abs/2202.10944 · HTML: https://mlsanity.com/paper/2202.10944/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 99 references that are in the map.
- First posted on arXiv 16 Feb 2022.

## Builds on (most cited first, 22 of 22)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Off-policy Bandits with Deficient Support](https://mlsanity.com/paper/2006.09438/) (2020)
- [Policy Evaluation and Optimization with Continuous Treatments](https://mlsanity.com/paper/1802.06037/) (2018)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [The Sample Complexity of Revenue Maximization](https://mlsanity.com/paper/1502.00963/) (2015)
- [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Optimization of Tree Ensembles](https://mlsanity.com/paper/1705.10883/) (2017)
- [Model Distillation for Revenue Optimization: Interpretable Personalized Pricing](https://mlsanity.com/paper/2007.01903/) (2020)
- [Revenue Optimization with Approximate Bid Predictions](https://mlsanity.com/paper/1706.04732/) (2017)
- [The Sample Complexity of Auctions with Side Information](https://mlsanity.com/paper/1511.02296/) (2015)
- [Optimal Policy Trees](https://mlsanity.com/paper/2012.02279/) (2020)
- [Learning Theory and Algorithms for Revenue Optimization in Second-Price Auctions with Reserve](https://mlsanity.com/paper/1310.5665/) (2013)
- [Making the Most of Your Samples](https://mlsanity.com/paper/1407.2479/) (2014)
- [Contextual Reserve Price Optimization in Auctions via Mixed-Integer Programming](https://mlsanity.com/paper/2002.08841/) (2020)
- [Model-Free Assortment Pricing with Transaction Data](https://mlsanity.com/paper/2101.02251/) (2021)
- [Loss Functions for Discrete Contextual Pricing with Observational Data](https://mlsanity.com/paper/2111.09933/) (2021)
- [Optimal Pricing with a Single Point](https://mlsanity.com/paper/2103.05611/) (2021)
- [Are Two (Samples) Really Better Than One? On the Non-Asymptotic Performance of Empirical Revenue Maximization](https://mlsanity.com/paper/1802.08037/) (2018)
- [Assortment Optimization under the Decision Forest Model](https://mlsanity.com/paper/2103.14067/) (2021)

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

- [Insurance Pricing Optimization via Off-Policy Evaluation](https://mlsanity.com/paper/2605.28327/) (2026)

## Abstract (arXiv)

We study an off-policy contextual pricing problem where the seller has access to samples of prices that customers were previously offered, whether they purchased at that price, and auxiliary features describing the customer and/or item being sold. This is in contrast to the well-studied setting in which samples of the customer's valuation (willingness to pay) are observed. In our setting, the observed data is influenced by the previous pricing policy, and we do not know how customers would have responded to alternative prices. We introduce suitable loss functions for this setting that can be directly optimized to find an effective pricing policy with expected revenue guarantees, without the need for estimation of an intermediate demand function. We focus on convex loss functions. This is particularly relevant when linear pricing policies are desired for interpretability reasons, resulting in a tractable convex revenue optimization problem. We propose generalized hinge and quantile pricing loss functions that price at a multiplicative factor of the conditional expected valuation or a particular quantile of the prices that sold, despite the valuation data not being observed. We prove expected revenue bounds for these pricing policies respectively when the valuation distribution is log-concave, and we provide generalization bounds for the finite sample case. Finally, we conduct simulations on both synthetic and real-world data to demonstrate that this approach is competitive with, and in some settings outperforms, state-of-the-art methods in contextual pricing.