  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.
