Preserving Privacy in Feature-based Newsvendor Problems with Unknown Demand

Core Concepts

A novel privacy-preserving algorithm is proposed to estimate the optimal inventory policy for feature-based newsvendor problems with unknown demand distribution, while providing provable privacy guarantees.

Abstract

The content presents a novel approach to estimate a privacy-preserving optimal inventory policy within the f-differential privacy framework for feature-based newsvendor problems with unknown demand distribution.
Key highlights:

Adopts the recently introduced f-differential privacy framework to establish rigorous privacy protection properties, overcoming limitations of the classical (ε,δ)-differential privacy.

Proposes a computationally efficient noisy clipped gradient descent algorithm based on convolution smoothing to simultaneously address the challenges of unknown demand distribution, nonsmooth loss function, provable privacy guarantees, and desirable statistical precision.

Derives finite-sample high-probability bounds for optimal policy parameter estimation and regret analysis. By leveraging the structure of the newsvendor problem, it attains a faster excess population risk bound compared to indiscriminate application of existing results for general nonsmooth convex loss.

Numerical experiments demonstrate that the proposed method can achieve desirable privacy protection with a marginal increase in cost.

Stats

"The optimal ordering level q(x) is set as a linear function of the feature vector x: q(x) = xTβ."
"The conditional τ-th quantile of the demand d given x is xTβ*, where τ = b/(b+h) and β* is the optimal parameter vector."

Quotes

"A key challenge is the nonsmoothness of the newsvendor loss function, which sets it apart from existing work on privacy-preserving algorithms in other settings."
"Our bound aligns with that for strongly convex and smooth loss function."

Key Insights Distilled From

Private Optimal Inventory Policy Learning for Feature-based Newsvendor with Unknown Demand

by Tuoyi Zhao,W... at arxiv.org 04-25-2024

https://arxiv.org/pdf/2404.15466.pdf

Deeper Inquiries

How can the proposed privacy-preserving algorithm be extended to handle more complex demand models beyond the linear structure

The proposed privacy-preserving algorithm can be extended to handle more complex demand models beyond the linear structure by incorporating non-linear functions or transformations of the features. Instead of assuming a linear relationship between the features and the demand, more sophisticated models such as polynomial functions, splines, or neural networks can be used to capture the non-linear patterns in the data. By introducing these non-linear transformations, the algorithm can adapt to more intricate demand structures and provide more accurate inventory policy estimations. Additionally, ensemble methods like random forests or gradient boosting can be employed to handle interactions between features and capture complex demand dynamics.

What are the potential limitations of the f-differential privacy framework in practical applications, and how can they be addressed

While the f-differential privacy framework offers several advantages such as exact composition properties and a clear hypothesis testing interpretation, there are potential limitations in practical applications. One limitation is the computational complexity associated with ensuring differential privacy, especially when dealing with large datasets or complex algorithms. This can lead to increased processing times and resource requirements, impacting the scalability of the privacy-preserving mechanisms. To address this, optimization techniques and algorithmic improvements can be implemented to enhance the efficiency of the privacy-preserving algorithms. Additionally, the trade-off between privacy protection and data utility needs to be carefully balanced to ensure that the level of privacy does not compromise the accuracy and effectiveness of the analysis.

What are the implications of the privacy-preserving inventory policy on the overall supply chain performance and customer experience

The implementation of a privacy-preserving inventory policy can have significant implications on the overall supply chain performance and customer experience. By safeguarding individual-level data and ensuring privacy protection, businesses can build trust with customers and stakeholders, leading to enhanced brand reputation and customer loyalty. Moreover, the adoption of privacy-preserving algorithms can mitigate the risk of data breaches and regulatory non-compliance, reducing potential financial and legal consequences. From a supply chain perspective, the optimized inventory policy derived from the privacy-preserving algorithm can improve operational efficiency, reduce inventory holding costs, and enhance demand forecasting accuracy. This, in turn, can lead to better inventory management, streamlined logistics, and ultimately, improved customer satisfaction through timely and accurate order fulfillment.