Differentially Private Linear Optimization for Multi-Party Resource Sharing

This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange information to obtain the optimal objective function value. This information bears private data from each party in terms of coefficients used in the mathematical program. Moreover, the parties also consider the individual optimal solutions as private. In this setting, the concern for the parties is the privacy of their data and their optimal allocations. We propose a two-step approach to meet the privacy requirements of the parties. In the first step, we obtain a reformulated model that is amenable to a decomposition scheme. Although this scheme eliminates almost all data exchanges, it does not provide a formal privacy guarantee. In the second step, we provide this guarantee with a locally differentially private algorithm, which does not need a trusted aggregator, at the expense of deviating slightly from the optimality. We provide bounds on this deviation and discuss the consequences of these theoretical results. We also propose a novel modification to increase the efficiency of the algorithm in terms of reducing the theoretical optimality gap. The study ends with a numerical experiment on a planning problem that demonstrates an application of the proposed approach. As we work with a general linear optimization model, our analysis and discussion can be used in different application areas including production planning, logistics, and revenue management

New Attacks against Transformation-Based Privacy-Preserving Linear Programming

In this paper we demonstrate a number of attacks against proposed protocols for privacy-preserving linear programming, based on publishing and solving a transformed version of the problem instance. Our attacks exploit the geometric structure of the problem, which has mostly been overlooked in the previous analyses and is largely preserved by the proposed transformations. The attacks are efficient in practice and cast serious doubt to the viability of transformation-based approaches in general

Insecurity of Transformation-Based Privacy-Preserving Linear Programming

Rakendusmatemaatikat kasutatakse paljudes reaalse maailma probleemides. Nende probleemide lahendamine võib olla seotud tundlike andmetega. Sellisel juhul läheb tarvis krüptograafilisi meetodeid. Kuigi on tõestatud, et iga funktsiooni saab arvutada turvaliselt, on küsimus selles, kuidas teha seda efektiivselt. Üldiselt võib olla keeruline lahendada optimeerimisülesandeid nii turvaliselt kui ka efektiivselt, kuid häid lahendeid saab leida kitsamatele ülesannete klassidele, näiteks lineaarse planeerimise ülesannetele. Käesolev töö annab ülevaate teisenduspõhisest privaatsust säilitavast lineaarsest planeerimisest, tutvustades mõningaid probleeme eelmistes töödes ja näidates teisenduspõhise meetodi ebaturvalisust. Töö esitab konkreetseid ründeid olemasolevate teisendusmeetodite vastu. Töös pakutakse välja võimalikud viisid nende rünnete eest kaitsmiseks ja seejärel näidatakse, et mõned teisenduspõhise meetodi puudused ei ole üldse ületatavad, vähemalt eelmistes töödes kasutatud teatud teisenduste klassi raamesse jäädes.Applied mathematics is used in many real-world problems. Solving some of these problems may involve sensitive data. In this case, cryptographic techniques become necessary. Although it has been proven that any function can be computed securely, it is still a question how to do it efficiently. While it may be difficult to solve optimization tasks securely and efficiently in general, there may still be solutions for some particular classes of tasks, such as linear programming. This thesis gives an overview of the transformation-based privacy-preserving linear programming. The thesis introduces some problems of this approach that have been present in the previous works and demonstrates its insecurity. It presents concrete attacks against published methods following this approach. Possible methods of protection against these attacks are proposed. It has been proven that there are issues that cannot be resolved at all using the particular known class of efficient transformations that has been used before

Privacy in resource allocation problems

Collaborative decision-making processes help parties optimize their operations, remain competitive in their markets, and improve their performances with environmental issues. However, those parties also want to keep their data private to meet their obligations regarding various regulations and not to disclose their strategic information to the competitors. In this thesis, we study collaborative capacity allocation among multiple parties and present that (near) optimal allocations can be realized while considering the parties' privacy concerns.We first attempt to solve the multi-party resource sharing problem by constructing a single model that is available to all parties. We propose an equivalent data-private model that meets the parties' data privacy requirements while ensuring optimal solutions for each party. We show that when the proposed model is solved, each party can only get its own optimal decisions and cannot observe others' solutions. We support our findings with a simulation study.The third and fourth chapters of this thesis focus on the problem from a different perspective in which we use a reformulation that can be used to distribute the problem among the involved parties. This decomposition lets us eliminate almost all the information-sharing requirements. In Chapter 3, together with the reformulated model, we benefit from a secure multi-party computation protocol that allows parties to disguise their shared information while attaining optimal allocation decisions. We conduct a simulation study on a planning problem and show our proposed algorithm in practice. We use the decomposition approach in Chapter 4 with a different privacy notion. We employ differential privacy as our privacy definition and design a differentially private algorithm for solving the multi-party resource sharing problem. Differential privacy brings in formal data privacy guarantees at the cost of deviating slightly from optimality. We provide bounds on this deviation and discuss the consequences of these theoretical results. We show the proposed algorithm on a planning problem and present insights about its efficiency.<br/

Practical Privacy-Preserving Multiparty Linear Programming Based on Problem Transformation

International audienceCryptographic solutions to privacy-preserving multi-party linear programming are slow. This makes them unsuitable for many economically important applications, such as supply chain optimization, whose size exceeds their practically feasible input range. In this paper we present a privacy-preserving transformation that allows secure outsourcing of the linear program computation in an efficient manner. We evaluate security by quantifying the leakage about the input after the transformation and present implementation results. Using this transformation, we can mostly replace the costly cryptographic operations and securely solve problems several orders of magnitude larger

Preservation of Patient Level Privacy: Federated Classification and Calibration Models

With the launching of the Precision Medicine Initiative in the United States, by the National Institute of Health, and the emergence of a large volume of electronic health records, there are many opportunities to improve clinical decision support systems. A large number of samples are needed to build predictive models that have adequate discrimination and calibration. However, protecting patient privacy is also an important issue. Patient data are typically protected in localized silos, and consolidation of datasets from different healthcare systems is difficult. Federated learning allows the training of a global model by amassing intermediate calculations from localized medical systems. The knowledge learned from the data can be transferred and aggregated to achieve better performance than the one achieved by individual local models. Federated learning may help build better models, providing more accurate predictions. There are two types of measures to assess how well a model performs: discrimination and calibration. While most papers report discrimination measures, calibration has often been neglected but it is a critical metric for evaluation. In this dissertation, I show a novel way to build classifiers and calibration models in a federated manner. I also show how I can evaluate and improve model calibration in this manner. Federated modeling enables the accumulation of knowledge and information that are otherwise locked behind local medical systems