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We consider differentially private algorithms for reinforcement learning incontinuous spaces, such that neighboring reward functions areindistinguishable. This protects the reward information from being exploited bymethods such as inverse reinforcement learning. Existing studies that guaranteedifferential privacy are not extendable to infinite state spaces, as the noiselevel to ensure privacy will scale accordingly to infinity. Our aim is toprotect the value function approximator, without regard to the number of statesqueried to the function. It is achieved by adding functional noise to the valuefunction iteratively in the training. We show rigorous privacy guarantees by aseries of analyses on the kernel of the noise space, the probabilistic bound ofsuch noise samples, and the composition over the iterations. We gain insightinto the utility analysis by proving the algorithm's approximate optimalitywhen the state space is discrete. Experiments corroborate our theoreticalfindings and show improvement over existing approaches.

Privacy-preserving Q-Learning with Functional Noise in Continuous State Spaces