  We consider a cloud-based control architecture in which the local plants
outsource the control synthesis task to the cloud. In particular, we consider a
cloud-based reinforcement learning (RL), where updating the value function is
outsourced to the cloud. To achieve confidentiality, we implement computations
over Fully Homomorphic Encryption (FHE). We use a CKKS encryption scheme and a
modified SARSA(0) reinforcement learning to incorporate the encryption-induced
delays. We then give a convergence result for the delayed updated rule of
SARSA(0) with a blocking mechanism. We finally present a numerical
demonstration via implementing on a classical pole-balancing problem.
