  A learner aims to minimize a function $f$ by repeatedly querying a
distributed oracle that provides noisy gradient evaluations. At the same time,
the learner seeks to hide $\arg\min f$ from a malicious eavesdropper that
observes the learner's queries. This paper considers the problem of
\textit{covert} or \textit{learner-private} optimization, where the learner has
to dynamically choose between learning and obfuscation by exploiting the
stochasticity. The problem of controlling the stochastic gradient algorithm for
covert optimization is modeled as a Markov decision process, and we show that
the dynamic programming operator has a supermodular structure implying that the
optimal policy has a monotone threshold structure. A computationally efficient
policy gradient algorithm is proposed to search for the optimal querying policy
without knowledge of the transition probabilities. As a practical application,
our methods are demonstrated on a hate speech classification task in a
federated setting where an eavesdropper can use the optimal weights to generate
toxic content, which is more easily misclassified. Numerical results show that
when the learner uses the optimal policy, an eavesdropper can only achieve a
validation accuracy of $52\%$ with no information and $69\%$ when it has a
public dataset with 10\% positive samples compared to $83\%$ when the learner
employs a greedy policy.
