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Semi-Parametric Contextual Pricing with General Smoothness

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.6Download Report PDF
Contextual pricing; online learning; semi-parametric models
Abstract:

We study the contextual pricing problem, where in each round a seller observes a context, sets a price, and receives a binary purchase signal. We adopt a semi-parametric model in which the demand follows a linear parametric form composed with an unknown link function from a β\beta-Hölder class. Prior work established regret rates of O~(T2/3)\tilde{\mathcal{O}}(T^{2/3}) for β=1\beta=1 and O~(T3/5)\tilde{\mathcal{O}}(T^{3/5}) for β=2\beta=2. Under a uni-modality condition, we propose a unified algorithm that combines the stationary subroutine of Wang & Chen (2025) with local polynomial regression, achieving the general rate O~(Tβ+12β+1)\tilde{\mathcal{O}}(T^{\frac{\beta+1}{2\beta+1}}) for all β≥1\beta \ge 1. This recovers and strengthens existing results, while also addressing a gap in the prior analysis for β=2\beta=2. Our analysis develops tighter semi-parametric confidence regions, removes derivative lower bound assumptions from earlier work, and offers a sharper exploration–exploitation trade-off. These insights not only extend theoretical guarantees to general β\beta but also improve practical performance by reducing the need for long forced-exploration phases.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes a unified algorithm for contextual pricing under semi-parametric demand models, achieving regret Õ(T^(β+1)/(2β+1)) for all β ≥ 1. It resides in the Generalized Semi-Parametric Structures leaf, which contains four papers including the original work. This leaf sits within the broader Semi-Parametric Demand Modeling Frameworks branch, indicating a moderately populated research direction focused on parametric components composed with unknown link functions. The taxonomy shows this is an active area with neighboring leaves exploring partially linear models and survival-based approaches.

The taxonomy reveals that Generalized Semi-Parametric Structures neighbors Partially Linear Demand Models (two papers) and Survival and Hazard-Based Models (two papers), all under the same parent branch. Adjacent branches include Nonparametric and Doubly Flexible Approaches and Contextual Bandits and Online Learning, suggesting the field balances structural assumptions with algorithmic tractability. The scope note for this leaf explicitly includes models with parametric components composed with unknown link functions or general smoothness classes, which aligns closely with the paper's β-Hölder class formulation. This positioning suggests the work extends an established modeling paradigm rather than introducing a fundamentally new framework.

Among seventeen candidates examined, the unified regret rate contribution shows one refutable candidate from seven examined, while the joint estimation procedure contribution found no refutations among ten candidates examined. The tighter confidence regions contribution was not examined against prior work. The limited search scope (seventeen candidates from a thirty-paper taxonomy) means these statistics reflect a focused semantic neighborhood rather than exhaustive coverage. The unified rate result appears to have more substantial prior work overlap, while the estimation procedure and confidence region analysis may offer more incremental refinement. The analysis explicitly notes this is based on top-K semantic search plus citation expansion, not comprehensive review.

Given the limited search scope and the paper's position in a moderately populated leaf with three sibling papers, the work appears to refine and extend existing semi-parametric pricing methods rather than opening entirely new territory. The contribution-level statistics suggest mixed novelty: the core regret rate has identifiable prior overlap, while technical improvements in confidence regions and estimation may be more distinctive. The taxonomy context indicates this is an active research direction where incremental theoretical advances are common and valued.

Taxonomy

Core-task Taxonomy Papers
30
3
Claimed Contributions
17
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: contextual dynamic pricing with semi-parametric demand models. The field balances flexibility in modeling consumer demand with the need for tractable, data-driven pricing algorithms. The taxonomy reveals several complementary directions. Semi-Parametric Demand Modeling Frameworks (including works like Partially Linear Demand[1] and Semiparametric Dynamic Pricing[3]) impose structure on part of the demand function while leaving other components nonparametric, enabling both interpretability and adaptability. Nonparametric and Doubly Flexible Approaches (e.g., Doubly Nonparametric Utility[2]) push further toward minimal assumptions, while Bayesian and Hierarchical Estimation Methods offer probabilistic inference under uncertainty. Machine Learning Integration and Hybrid Approaches blend classical econometric structures with modern predictive tools, and Robust and Distributional Uncertainty Methods (such as Randomized Robust Price[8]) address model misspecification. Contextual Bandits and Online Learning branches focus on sequential decision-making with exploration-exploitation trade-offs, Causal Inference and Confounding Mitigation tackles endogeneity issues, and Domain-Specific Applications (e.g., Electricity Pricing Review[12], Fresh Retail Markdowns[18]) tailor methods to particular industries. Econometric Foundations anchor the taxonomy in classical estimation theory. A particularly active line of work explores how to relax parametric assumptions without sacrificing regret guarantees or computational efficiency. Studies like Tight Regret Bounds[6] and Semiparametric Policy Optimization[5] investigate whether semi-parametric structures can achieve near-optimal performance in online settings, while others examine shape constraints (Shape Restricted Demands[17], S-Concave Demand[11]) to preserve economic intuition. Semiparametric Contextual Pricing[0] sits within the Generalized Semi-Parametric Structures cluster, closely aligned with Semiparametric Dynamic Pricing[3] and neighboring Semiparametric Policy Optimization[5]. Compared to these works, Semiparametric Contextual Pricing[0] emphasizes a particular decomposition of demand that balances known functional forms with flexible nonparametric components, aiming to improve both statistical efficiency and algorithmic tractability. This positioning reflects ongoing debates about how much structure to impose and where flexibility matters most for real-world pricing applications.

Claimed Contributions

Unified algorithm achieving Õ(T^(β+1)/(2β+1)) regret for all β ≥ 1

The authors develop a unified algorithmic framework that achieves regret rate Õ(T^(β+1)/(2β+1)) for all smoothness parameters β ≥ 1 in semi-parametric contextual pricing. This recovers and strengthens existing results for β = 1 and β = 2, and interpolates to the parametric rate as β approaches infinity.

7 retrieved papers
Can Refute
Tighter semi-parametric confidence regions via improved analysis

The authors provide an improved confidence bound analysis that generalizes prior work, removes the strictly increasing CDF condition required in previous smooth semi-parametric settings, and achieves a sharper exploration-exploitation trade-off by reducing the forced-exploration phase length.

0 retrieved papers
Joint estimation procedure using local polynomial regression

The authors introduce a unified joint estimation procedure that combines piloted local polynomial regression with constrained least-squares refinement to simultaneously estimate both parametric and non-parametric components of the demand model for general smoothness β ≥ 1.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Unified algorithm achieving Õ(T^(β+1)/(2β+1)) regret for all β ≥ 1

The authors develop a unified algorithmic framework that achieves regret rate Õ(T^(β+1)/(2β+1)) for all smoothness parameters β ≥ 1 in semi-parametric contextual pricing. This recovers and strengthens existing results for β = 1 and β = 2, and interpolates to the parametric rate as β approaches infinity.

Contribution

Tighter semi-parametric confidence regions via improved analysis

The authors provide an improved confidence bound analysis that generalizes prior work, removes the strictly increasing CDF condition required in previous smooth semi-parametric settings, and achieves a sharper exploration-exploitation trade-off by reducing the forced-exploration phase length.

Contribution

Joint estimation procedure using local polynomial regression

The authors introduce a unified joint estimation procedure that combines piloted local polynomial regression with constrained least-squares refinement to simultaneously estimate both parametric and non-parametric components of the demand model for general smoothness β ≥ 1.

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