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

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.

💡 Research Summary

The paper tackles the challenging problem of dynamic pricing in high‑dimensional e‑commerce markets, where a seller must repeatedly set prices for thousands of products while learning uncertain demand functions. Existing contextual bandit approaches that rely on low‑rank latent representations achieve low regret but sacrifice interpretability because the latent factors do not correspond to observable product attributes. To bridge this gap, the authors introduce an Additive Feature Decomposition‑based Low‑Dimensional Demand (AFDLD) model and a corresponding online learning algorithm called ADEPT (Additive DEcomposition for Pricing with cross‑elasticity and Time‑adaptive learning).

AFDLD model.
Each product is described by a known feature vector (u_i\in\mathbb R^d) (e.g., storage size, camera megapixels, brand). Prices are expressed as a linear combination of attribute‑level price coefficients (\theta\in\mathbb R^d): \