"We started to establish a new fundamental theory for privacy preserving distributed optimization" with Carlo Fischione

Sovereign state governments, national and international banks and companies in a free market, hospitals, members of social networks, electors, electrical distribution companies and local electrical producers, wireless devices, are all typical networked parties that have to collaborate for huge mutual benefit while the transactions among them must be private. For example, wireless devices may cooperatively compute the best routing path for downloading some multimedia content, or send sensitive data to the cloud to receive back services, without disclosing private information. Hospitals could merge their patient data sets, which contain highly private information, to better classify, derive patient state correlations, and make risk predictions, which is currently not allowed in many European and North American countries due to privacy restrictions.

Any collaboration among parties for computations in networking, classification, estimation, learning, control, logistics, etc., is ultimately based on mathematical distributed optimization problems, the solution of which requires data sharing among these parties. Unfortunately, the classic approach to preserve privacy, cryptography, introduces formidable overheads and heavy coordinations in distributed optimization, which substantially prevents or makes it impossible collaboration. Actually, such a difficulty is exactly encountered when merging medical data sets of different hospitals for inference purposes. Yet such a collaboration would entail great benefits for society if conducted properly. The fundamental question is how to quickly solve distributed optimization problems among parties that are unwilling or cannot share their sensitive data and that yet would receive much benefit by a collaboration.

In this research project, we started to establish a new fundamental theory for privacy preserving distributed optimization. The growing size, complexity, and heterogeneity of networks makes it simply essential the availability of fast and private distributed solution methods. The development of such a theory would posses many appealing aspects, e.g., efficiency, scalability, natural geographical distribution of problem data. It would offer highly desirable privacy-preserving properties without requiring the huge extra coordination or overhead required by cryptography. 

The development of a new theory of per se privacy preserving optimization will have a huge impact in the scientific community as well as in the society. Privacy and distributed optimization are currently regarded (separately) as some of the most relevant research topics in control theory, signal processing theory, wireless communication, computer sciences, etc. There is an evident gap between privacy and optimization. From a fundamental research point of view, this theory is certainly at its infancy.

We believe our results will enable many applications that are currently not allowed by cryptography, with exceptional benefits in the society: for example, medical data could be privately shared among hospitals to perform inference (which is not allowed today due to privacy concerns), thus leading to better medical treatments and potentially saving of many lives. Insurance companies would be able to privately merge their data set to reduce the risks and thus offering cheaper premium with huge cost savings. Future heterogeneous wireless networks will have to be operated by distributed optimal algorithms that maintain the privacy of the users and personal data.