Matteo Sordello

Matteo Sordello, Zhiqi Bu, Jinshuo Dong

In this paper, we consider the framework of privacy amplification via iteration, which is originally proposed by Feldman et al. and subsequently simplified by Asoodeh et al. in their analysis via the contraction coefficient. This line of work focuses on the study of the privacy guarantees obtained by the projected noisy stochastic gradient descent (PNSGD) algorithm with hidden intermediate updates. A limitation in the existing literature is that only the early stopped PNSGD has been studied, while no result has been proved on the more widely-used PNSGD applied on a shuffled dataset. Moreover, no scheme has been yet proposed regarding how to decrease the injected noise when new data are received in an online fashion. In this work, we first prove a privacy guarantee for shuffled PNSGD, which is investigated asymptotically when the noise is fixed for each sample size $n$ but reduced at a predetermined rate when $n$ increases, in order to achieve the convergence of privacy loss. We then analyze the online setting and provide a faster decaying scheme for the magnitude of the injected noise that also guarantees the convergence of privacy loss.

Matteo Sordello, Niccolò Dalmasso, Hangfeng He et al.

This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is detected, that is, the iterates are likely to bounce at around a vicinity of a local minimum. The detection is performed by splitting the single thread into two and using the inner product of the gradients from the two threads as a measure of stationarity. Owing to this simple yet provably valid stationarity detection, SplitSGD is easy-to-implement and essentially does not incur additional computational cost than standard SGD. Through a series of extensive experiments, we show that this method is appropriate for both convex problems and training (non-convex) neural networks, with performance compared favorably to other stochastic optimization methods. Importantly, this method is observed to be very robust with a set of default parameters for a wide range of problems and, moreover, can yield better generalization performance than other adaptive gradient methods such as Adam.