Enabling Data Exchange in Interactive State Estimation under Privacy Constraints

TL;DR

This paper investigates mechanisms for data sharing among agents in large networks, balancing privacy and estimation accuracy, and proposes centralized and decentralized strategies to enable meaningful data exchange under privacy constraints.

Contribution

It introduces centralized and decentralized game-theoretic mechanisms that facilitate data exchange while respecting privacy limits in distributed state estimation.

Findings

Distributed policies enable non-trivial data sharing within certain fidelity ranges.

Repeated game strategies naturally sustain data exchange without central control.

Optimal policies balance privacy leakage and estimation fidelity effectively.

Abstract

Data collecting agents in large networks, such as the electric power system, need to share information (measurements) for estimating the system state in a distributed manner. However, privacy concerns may limit or prevent this exchange leading to a tradeoff between state estimation fidelity and privacy (referred to as competitive privacy). This paper builds upon a recent information-theoretic result (using mutual information to measure privacy and mean-squared error to measure fidelity) that quantifies the region of achievable distortion-leakage tuples in a two-agent network. The objective of this paper is to study centralized and decentralized mechanisms that can enable and sustain non-trivial data exchanges among the agents. A centralized mechanism determines the data sharing policies that optimize a network-wide objective function combining the fidelities and leakages at both agents. Using common-goal games and best-response analysis, the optimal policies allow for distributed implementation. In contrast, in the decentralized setting, repeated discounted games are shown to naturally enable data exchange without any central control nor economic incentives. The effect of repetition is modeled by a time-averaged payoff function at each agent which combines its fidelity and leakage at each interaction stage. For both approaches, it is shown that non-trivial data exchange can be sustained for specific fidelity ranges even when privacy is a limiting factor.