Privacy-preserving Q-Learning with Functional Noise in Continuous State Spaces
This addresses privacy concerns in reinforcement learning for applications like robotics or healthcare, where reward functions must be protected from exploitation, though it is incremental as it builds on existing differential privacy frameworks.
The paper tackles the problem of ensuring differential privacy in reinforcement learning with continuous state spaces, where existing methods fail due to infinite noise scaling, by adding functional noise to the value function during training, achieving rigorous privacy guarantees and showing approximate optimality in discrete cases with experimental improvements.
We consider differentially private algorithms for reinforcement learning in continuous spaces, such that neighboring reward functions are indistinguishable. This protects the reward information from being exploited by methods such as inverse reinforcement learning. Existing studies that guarantee differential privacy are not extendable to infinite state spaces, as the noise level to ensure privacy will scale accordingly to infinity. Our aim is to protect the value function approximator, without regard to the number of states queried to the function. It is achieved by adding functional noise to the value function iteratively in the training. We show rigorous privacy guarantees by a series of analyses on the kernel of the noise space, the probabilistic bound of such noise samples, and the composition over the iterations. We gain insight into the utility analysis by proving the algorithm's approximate optimality when the state space is discrete. Experiments corroborate our theoretical findings and show improvement over existing approaches.