On Reconstructability of Quadratic Utility Functions from the Iterations in Gradient Methods

TL;DR

This paper investigates the conditions under which an eavesdropper can reconstruct quadratic utility functions from gradient algorithm iterations, and proposes step-size rules to prevent such reconstruction, enhancing privacy.

Contribution

It provides conditions and step-size guidelines that make reconstructing quadratic utility functions from gradient iterations practically impossible for certain Bayesian filters.

Findings

Proper step-size selection prevents utility function reconstruction.

Reconstruction is feasible only with certain step-size choices.

Guidelines for secure gradient algorithm implementation are established.

Abstract

In this paper, we consider a scenario where an eavesdropper can read the content of messages transmitted over a network. The nodes in the network are running a gradient algorithm to optimize a quadratic utility function where such a utility optimization is a part of a decision making process by an administrator. We are interested in understanding the conditions under which the eavesdropper can reconstruct the utility function or a scaled version of it and, as a result, gain insight into the decision-making process. We establish that if the parameter of the gradient algorithm, i.e.,~the step size, is chosen appropriately, the task of reconstruction becomes practically impossible for a class of Bayesian filters with uniform priors. We establish what step-size rules should be employed to ensure this.