  This paper studies how a stochastic gradient algorithm (SG) can be controlled
to hide the estimate of the local stationary point from an eavesdropper. Such
problems are of significant interest in distributed optimization settings like
federated learning and inventory management. A learner queries a stochastic
oracle and incentivizes the oracle to obtain noisy gradient measurements and
perform SG. The oracle probabilistically returns either a noisy gradient of the
function} or a non-informative measurement, depending on the oracle state and
incentive. The learner's query and incentive are visible to an eavesdropper who
wishes to estimate the stationary point. This paper formulates the problem of
the learner performing covert optimization by dynamically incentivizing the
stochastic oracle and obfuscating the eavesdropper as a finite-horizon Markov
decision process (MDP). Using conditions for interval-dominance on the cost and
transition probability structure, we show that the optimal policy for the MDP
has a monotone threshold structure. We propose searching for the optimal
stationary policy with the threshold structure using a stochastic approximation
algorithm and a multi-armed bandit approach. The effectiveness of our methods
is numerically demonstrated on a covert federated learning hate-speech
classification task.
