Bei Jiang

Enze Shi, Jinhan Xie, Bei Jiang et al.

Differentially Private Stochastic Gradient Descent (DP-SGD) has been widely used for solving optimization problems with privacy guarantees in machine learning and statistics. Despite this, a systematic non-asymptotic convergence analysis for DP-SGD, particularly in the context of online problems and local differential privacy (LDP) models, remains largely elusive. Existing non-asymptotic analyses have focused on non-private optimization methods, and hence are not applicable to privacy-preserving optimization problems. This work initiates the analysis to bridge this gap and opens the door to non-asymptotic convergence analysis of private optimization problems. A general framework is investigated for the online LDP model in stochastic optimization problems. We assume that sensitive information from individuals is collected sequentially and aim to estimate, in real-time, a static parameter that pertains to the population of interest. Most importantly, we conduct a comprehensive non-asymptotic convergence analysis of the proposed estimators in finite-sample situations, which gives their users practical guidelines regarding the effect of various hyperparameters, such as step size, parameter dimensions, and privacy budgets, on convergence rates. Our proposed estimators are validated in the theoretical and practical realms by rigorous mathematical derivations and carefully constructed numerical experiments.

Ke Sun, Yafei Wang, Yi Liu et al.

Anderson mixing has been heuristically applied to reinforcement learning (RL) algorithms for accelerating convergence and improving the sampling efficiency of deep RL. Despite its heuristic improvement of convergence, a rigorous mathematical justification for the benefits of Anderson mixing in RL has not yet been put forward. In this paper, we provide deeper insights into a class of acceleration schemes built on Anderson mixing that improve the convergence of deep RL algorithms. Our main results establish a connection between Anderson mixing and quasi-Newton methods and prove that Anderson mixing increases the convergence radius of policy iteration schemes by an extra contraction factor. The key focus of the analysis roots in the fixed-point iteration nature of RL. We further propose a stabilization strategy by introducing a stable regularization term in Anderson mixing and a differentiable, non-expansive MellowMax operator that can allow both faster convergence and more stable behavior. Extensive experiments demonstrate that our proposed method enhances the convergence, stability, and performance of RL algorithms.

Chenglin Li, Carrie Lu Tong, Di Niu et al.

Deep learning models for human activity recognition (HAR) based on sensor data have been heavily studied recently. However, the generalization ability of deep models on complex real-world HAR data is limited by the availability of high-quality labeled activity data, which are hard to obtain. In this paper, we design a similarity embedding neural network that maps input sensor signals onto real vectors through carefully designed convolutional and LSTM layers. The embedding network is trained with a pairwise similarity loss, encouraging the clustering of samples from the same class in the embedded real space, and can be effectively trained on a small dataset and even on a noisy dataset with mislabeled samples. Based on the learned embeddings, we further propose both nonparametric and parametric approaches for activity recognition. Extensive evaluation based on two public datasets has shown that the proposed similarity embedding network significantly outperforms state-of-the-art deep models on HAR classification tasks, is robust to mislabeled samples in the training set, and can also be used to effectively denoise a noisy dataset.

Donglai Zhu, Hengshuai Yao, Bei Jiang et al.

In deep neural network, the cross-entropy loss function is commonly used for classification. Minimizing cross-entropy is equivalent to maximizing likelihood under assumptions of uniform feature and class distributions. It belongs to generative training criteria which does not directly discriminate correct class from competing classes. We propose a discriminative loss function with negative log likelihood ratio between correct and competing classes. It significantly outperforms the cross-entropy loss on the CIFAR-10 image classification task.