[Paper Review] Model Distillation for Revenue Optimization: Interpretable Personalized Pricing

Max Biggs, Wei Sun+1 more|arXiv (Cornell University)|Jul 3, 2020

Explainable Artificial Intelligence (XAI)47 references30 citations

TL;DR

The paper studies using knowledge distillation in revenue-optimizing, interpretable pricing trees, highlighting potential pitfalls of naive regression-tree approaches and proposing prescriptive trees that maximize revenue.

ABSTRACT

Data-driven pricing strategies are becoming increasingly common, where customers are offered a personalized price based on features that are predictive of their valuation of a product. It is desirable for this pricing policy to be simple and interpretable, so it can be verified, checked for fairness, and easily implemented. However, efforts to incorporate machine learning into a pricing framework often lead to complex pricing policies which are not interpretable, resulting in slow adoption in practice. We present a customized, prescriptive tree-based algorithm that distills knowledge from a complex black-box machine learning algorithm, segments customers with similar valuations and prescribes prices in such a way that maximizes revenue while maintaining interpretability. We quantify the regret of a resulting policy and demonstrate its efficacy in applications with both synthetic and real-world datasets.

Motivation & Objective

• Motivate the need for interpretable, prescriptive pricing models in revenue optimization.
• Show pitfalls of naive teacher-student distillation when the goal is revenue maximization.
• Propose a prescriptive tree framework that directly optimizes revenue.
• Compare prescriptive trees to naive regression-tree approaches in toy and synthetic settings.

Proposed method

• Use a teacher-student distillation perspective to model demand and price effects.
• Demonstrate with a toy example that naive regression trees can underperform prescriptive trees for revenue.
• Develop a depth-k axis-aligned binary tree that partitions feature space into hyperrectangles to maximize revenue in each leaf.
• Provide a theoretical regret bound showing how tree depth and partitioning affect performance.
• Conduct synthetic experiments to compare prescriptive trees with alternative distillation approaches.
• Discuss preprocessing steps and discretization used for real data (Dunnhumby) in price personalization.

Experimental results

Research questions

• RQ1 Can prescriptive decision trees directly maximize revenue better than naive regression trees in pricing settings?
• RQ2 What is the impact of tree depth and data partitioning on revenue performance?
• RQ3 How does a distillation-based approach fare against traditional prescriptive methods in toy and synthetic scenarios?
• RQ4 What are the practical considerations for applying prescriptive pricing with real-world data (e.g., price discretization, demand inelasticity)?

Key findings

• A naive regression-tree approach can yield about half the revenue of a prescriptive tree in a toy inelastic-demand setting.
• A prescriptive tree that directly optimizes revenue achieves higher revenue than regressor-based distillation methods across synthetic datasets.
• Increasing tree depth improves revenue up to a point, with prescriptive trees outperforming naive approaches.
• Distillation-based alternatives that only mimic the teacher’s demand predictions require much greater depth to achieve comparable revenue and still underperform prescriptive trees.
• The supplementary material illustrates the potential pitfall of applying student-teacher frameworks naively to prescriptive problems.