On Reconstructability of Quadratic Utility Functions from the Iterations in Gradient Methods
This addresses security concerns for decision-making processes in networked optimization, though it is incremental as it builds on existing gradient method and eavesdropper analysis.
The paper tackles the problem of preventing an eavesdropper from reconstructing a quadratic utility function from gradient method iterations transmitted over a network, establishing that with appropriate step-size rules, reconstruction becomes practically impossible for a class of Bayesian filters.
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.