  Temporal difference (TD) learning is a widely used method to evaluate
policies in reinforcement learning. While many TD learning methods have been
developed in recent years, little attention has been paid to preserving privacy
and most of the existing approaches might face the concerns of data privacy
from users. To enable complex representative abilities of policies, in this
paper, we consider preserving privacy in TD learning with nonlinear value
function approximation. This is challenging because such a nonlinear problem is
usually studied in the formulation of stochastic nonconvex-strongly-concave
optimization to gain finite-sample analysis, which would require simultaneously
preserving the privacy on primal and dual sides. To this end, we employ a
momentum-based stochastic gradient descent ascent to achieve a single-timescale
algorithm, and achieve a good trade-off between meaningful privacy and utility
guarantees of both the primal and dual sides by perturbing the gradients on
both sides using well-calibrated Gaussian noises. As a result, our DPTD
algorithm could provide $(\epsilon,\delta)$-differential privacy (DP) guarantee
for the sensitive information encoded in transitions and retain the original
power of TD learning, with the utility upper bounded by
$\widetilde{\mathcal{O}}(\frac{(d\log(1/\delta))^{1/8}}{(n\epsilon)^{1/4}})$
(The tilde in this paper hides the log factor.), where $n$ is the trajectory
length and $d$ is the dimension. Extensive experiments conducted in OpenAI Gym
show the advantages of our proposed algorithm.
