Despite this appealing property in isolation, there has not been a systematic study on how to use them in conjunction with other differentially private mechanisms.

There is a disconnect between how researchers and practitioners handle privacy-utility tradeoffs.

In many practical applications of differential privacy, practitioners seek to provide the best privacy guarantees subject to a target level of accuracy. A recent line of work by Ligett et al. '17 and Whitehouse et al. '22 has developed such accuracy-first mechanisms by leveraging the idea of noise reduction that adds correlated noise to the sufficient statistic in a private computation and produces a sequence of increasingly accurate answers. A major advantage of noise reduction mechanisms is that the analysts only pay the privacy cost of the least noisy or most accurate answer released. Despite this appealing property in isolation, there has not been a systematic study on how to use them in conjunction with other differentially private mechanisms. A fundamental challenge is that the privacy guarantee for noise reduction mechanisms is (necessarily) formulated as ex-post privacy that bounds the privacy loss as a function of the released outcome. Furthermore, there has yet to be any study on how ex-post private mechanisms compose, which allows us to track the accumulated privacy over several mechanisms. We develop privacy filters [Rogers et al. '16, Feldman and Zrnic '21, and Whitehouse et al. '22'] that allow an analyst to adaptively switch between differentially private and ex-post private mechanisms subject to an overall differential privacy guarantee.

There is a disconnect between how researchers and practitioners handle privacy-utility tradeoffs. Researchers primarily operate from a privacy first perspective, setting strict privacy requirements and minimizing risk subject to these constraints. Practitioners often desire an accuracy first perspective, possibly satisfied with the greatest privacy they can get subject to obtaining sufficiently small error. Ligett et al. have introduced a "noise reduction" algorithm to address the latter perspective. The authors show that by adding correlated Laplace noise and progressively reducing it on demand, it is possible to produce a sequence of increasingly accurate estimates of a private parameter while only paying a privacy cost for the least noisy iterate released. In this work, we generalize noise reduction to the setting of Gaussian noise, introducing the Brownian mechanism. The Brownian mechanism works by first adding Gaussian noise of high variance corresponding to the final point of a simulated Brownian motion. Then, at the practitioner's discretion, noise is gradually decreased by tracing back along the Brownian path to an earlier time. Our mechanism is more naturally applicable to the common setting of bounded $\ell_2$-sensitivity, empirically outperforms existing work on common statistical tasks, and provides customizable control of privacy loss over the entire interaction with the practitioner. We complement our Brownian mechanism with ReducedAboveThreshold, a generalization of the classical AboveThreshold algorithm that provides adaptive privacy guarantees. Overall, our results demonstrate that one can meet utility constraints while still maintaining strong levels of privacy.

Deep reinforcement learning has been applied more and more widely nowadays, especially in various complex control tasks. Effective exploration for noisy networks is one of the most important issues in deep reinforcement learning. Noisy networks tend to produce stable outputs for agents. However, this tendency is not always enough to find a stable policy for an agent, which decreases efficiency and stability during the learning process. Based on NoisyNets, this paper proposes an algorithm called NROWAN-DQN, i.e., Noise Reduction and Online Weight Adjustment NoisyNet-DQN. Firstly, we develop a novel noise reduction method for NoisyNet-DQN to make the agent perform stable actions. Secondly, we design an online weight adjustment strategy for noise reduction, which improves stable performance and gets higher scores for the agent. Finally, we evaluate this algorithm in four standard domains and analyze properties of hyper-parameters. Our results show that NROWAN-DQN outperforms prior algorithms in all these domains. In addition, NROWAN-DQN also shows better stability. The variance of the NROWAN-DQN score is significantly reduced, especially in some action-sensitive environments. This means that in some environments where high stability is required, NROWAN-DQN will be more appropriate than NoisyNets-DQN.