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Learning to Price: Interpretable Attribute-Level Models for Dynamic Markets

Srividhya Sethuraman, Chandrashekar Lakshminarayanan

TL;DR

This work designs an interpretable, attribute-driven approach to dynamic pricing in high-dimensional markets. By introducing the Additive Feature Decomposition (AFD) framework and the AFDLD model, it captures substitution effects and yields a low-dimensional, transparent price representation p(i) = u(i)^T theta. Building on this, ADEPT provides a projection-free online learner operating in attribute space, achieving a sublinear regret of $\tilde{O}(\sqrt{d}\,T^{3/4})$ and demonstrating rapid adaptation to shocks and drifts. Empirical results on real datasets validate the additive structure, show competitive performance against baselines, and confirm the interpretability of attribute-level price explanations. Overall, the paper reconciles interpretability with efficiency in autonomous pricing through a structured, attribute-centric formulation and analysis.

Abstract

Dynamic pricing in high-dimensional markets poses fundamental challenges of scalability, uncertainty, and interpretability. Existing low-rank bandit formulations learn efficiently but rely on latent features that obscure how individual product attributes influence price. We address this by introducing an interpretable \emph{Additive Feature Decomposition-based Low-Dimensional Demand (\textbf{AFDLD}) model}, where product prices are expressed as the sum of attribute-level contributions and substitution effects are explicitly modeled. Building on this structure, we propose \textbf{ADEPT} (Additive DEcomposition for Pricing with cross-elasticity and Time-adaptive learning)-a projection-free, gradient-free online learning algorithm that operates directly in attribute space and achieves a sublinear regret of $\tilde{\mathcal{O}}(\sqrt{d}T^{3/4})$. Through controlled synthetic studies and real-world datasets, we show that ADEPT (i) learns near-optimal prices under dynamic market conditions, (ii) adapts rapidly to shocks and drifts, and (iii) yields transparent, attribute-level price explanations. The results demonstrate that interpretability and efficiency in autonomous pricing agents can be achieved jointly through structured, attribute-driven representations.

Learning to Price: Interpretable Attribute-Level Models for Dynamic Markets

TL;DR

This work designs an interpretable, attribute-driven approach to dynamic pricing in high-dimensional markets. By introducing the Additive Feature Decomposition (AFD) framework and the AFDLD model, it captures substitution effects and yields a low-dimensional, transparent price representation p(i) = u(i)^T theta. Building on this, ADEPT provides a projection-free online learner operating in attribute space, achieving a sublinear regret of and demonstrating rapid adaptation to shocks and drifts. Empirical results on real datasets validate the additive structure, show competitive performance against baselines, and confirm the interpretability of attribute-level price explanations. Overall, the paper reconciles interpretability with efficiency in autonomous pricing through a structured, attribute-centric formulation and analysis.

Abstract

Dynamic pricing in high-dimensional markets poses fundamental challenges of scalability, uncertainty, and interpretability. Existing low-rank bandit formulations learn efficiently but rely on latent features that obscure how individual product attributes influence price. We address this by introducing an interpretable \emph{Additive Feature Decomposition-based Low-Dimensional Demand (\textbf{AFDLD}) model}, where product prices are expressed as the sum of attribute-level contributions and substitution effects are explicitly modeled. Building on this structure, we propose \textbf{ADEPT} (Additive DEcomposition for Pricing with cross-elasticity and Time-adaptive learning)-a projection-free, gradient-free online learning algorithm that operates directly in attribute space and achieves a sublinear regret of . Through controlled synthetic studies and real-world datasets, we show that ADEPT (i) learns near-optimal prices under dynamic market conditions, (ii) adapts rapidly to shocks and drifts, and (iii) yields transparent, attribute-level price explanations. The results demonstrate that interpretability and efficiency in autonomous pricing agents can be achieved jointly through structured, attribute-driven representations.
Paper Structure (41 sections, 6 theorems, 28 equations, 7 figures, 5 tables, 4 algorithms)

This paper contains 41 sections, 6 theorems, 28 equations, 7 figures, 5 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Additive Feature Decomposition (AFD) of product prices
  3. Additive feature decomposition (AFD)
  4. Related Work
  5. AFDLD: A Novel Interpretable Low-Dimensional Demand Model
  6. Revenue as a Quadratic Form.
  7. Interpretability of AFDLD Model
  8. Experiment 1: Non-overlapping attributes (Table \ref{['tab:adept_exp_results1']}).
  9. Experiment 2: Overlapping attributes (Table \ref{['tab:adept_exp_results2']}).
  10. Experiment 1: Non-overlapping attributes (\ref{['tab:adept_diagV1']}).
  11. Experiment 2: Overlapping attributes (\ref{['tab:adept_diagV2']}).
  12. ADEPT: A Novel Dynamic Pricing Algorithm
  13. OPOK Vs. ADEPT
  14. Summary.
  15. Experiments and Insights
  16. ...and 26 more sections

Key Result

Proposition 1

The objective $-R_t(\theta_t)$ is convex in $\theta_t$.

Figures (7)

  • Figure 1: Illustration of additive feature-based price decomposition across domains.
  • Figure 2: Illustration of AFD representation where interpretable attributes combine additively to form transparent, feature-level price components.
  • Figure 3: Additive feature contributions to unit prices in the Dunnhumby grocery dataset, obtained via linear regression coefficients.
  • Figure 4: Additive feature contributions to prices in the H&M fashion dataset, highlighting interpretable price drivers such as garment type and season.
  • Figure 5: Cumulative regret (mean $\pm$ s.d.) over $T{=}50{,}000$ rounds. Top-left: S1 Stationary; top-right: S2 Shocks (vertical dashed lines mark change points); bottom-left: S3 Drifting; bottom-right: S4 Misspecified. All methods share the same price ball and comparator.
  • ...and 2 more figures

Theorems & Definitions (7)

  • Definition 1: Product–Feature Matrix
  • Proposition 1: Convex Optimization
  • Theorem 1
  • lemma 1: $M_1$ is PSD
  • Theorem 2: PSD/PD characterization
  • corollary 1: Strict diagonal dominance $\Rightarrow$ PD
  • corollary 2: Convexity