Collaborative learning has received huge interests due to its capability of exploiting the collective computing power of the wireless edge devices. However, during the learning process, model updates using local private samples and large-scale parameter exchanges among agents impose severe privacy concerns and communication bottleneck. In this paper, to address these problems, we propose two differentially private (DP) and communication efficient algorithms, called Q-DPSGD-1 and Q-DPSGD-2. In Q-DPSGD-1, each agent first performs local model updates by a DP gradient descent method to provide the DP guarantee and then quantizes the local model before transmitting it to neighbors to improve communication efficiency. In Q-DPSGD-2, each agent injects discrete Gaussian noise to enforce DP guarantee after first quantizing the local model. Moreover, we track the privacy loss of both approaches under the Renyi DP and provide convergence analysis for both convex and non-convex loss functions. The proposed methods are evaluated in extensive experiments on real-world datasets and the empirical results validate our theoretical findings.

Neural networks have become popular recently in recommendation systems to extract user and item representations. Most previous works follow a two-branch setting, where user and item networks learn user and item representations in the first and second branches, respectively. In the item cold-start problem, where the usage patterns of the items do not exist, the user network uses ID/interaction vector as the input and the item network uses the item side information (content) as the input. In this paper, we will show that by using this structure, two representations are learned for each item in the training set; one is the output of the item network and the other one is hidden inside the user network and is used for learning user representations. Learning two representations makes training slower and optimization more difficult. We propose to unify the two representations and only use the one generated by the item network. Also, we will show how attention mechanisms fit in our setting and how they can improve the quality of the representations. Our results on public and real-world datasets show that our approach converges faster, achieves higher recall in fewer iterations, and is more robust to the changes in the number of training samples compared to the previous works.

We propose a hard thresholding method based on stochastically controlled stochastic gradients (SCSG-HT) to solve a family of sparsity-constrained empirical risk minimization problems. The SCSG-HT uses batch gradients where batch size is pre-determined by the desirable precision tolerance rather than full gradients to reduce the variance in stochastic gradients. It also employs the geometric distribution to determine the number of loops per epoch. We prove that, similar to the latest methods based on stochastic gradient descent or stochastic variance reduction methods, SCSG-HT enjoys a linear convergence rate. However, SCSG-HT now has a strong guarantee to recover the optimal sparse estimator. The computational complexity of SCSG-HT is independent of sample size n when n is larger than 1/ε, which enhances the scalability to massive-scale problems. Empirical results demonstrate that SCSG-HT outperforms several competitors and decreases the objective value the most with the same computational costs.

The Alternating Direction Method of Multipliers (ADMM) and its distributed version have been widely used in machine learning. In the iterations of ADMM, model updates using local private data and model exchanges among agents impose critical privacy concerns. Despite some pioneering works to relieve such concerns, differentially private ADMM still confronts many research challenges. For example, the guarantee of differential privacy (DP) relies on the premise that the optimality of each local problem can be perfectly attained in each ADMM iteration, which may never happen in practice. The model trained by DP ADMM may have low prediction accuracy. In this paper, we address these concerns by proposing a novel (Improved) Plausible differentially Private ADMM algorithm, called PP-ADMM and IPP-ADMM. In PP-ADMM, each agent approximately solves a perturbed optimization problem that is formulated from its local private data in an iteration, and then perturbs the approximate solution with Gaussian noise to provide the DP guarantee. To further improve the model accuracy and convergence, an improved version IPP-ADMM adopts sparse vector technique (SVT) to determine if an agent should update its neighbors with the current perturbed solution. The agent calculates the difference of the current solution from that in the last iteration, and if the difference is larger than a threshold, it passes the solution to neighbors; or otherwise the solution will be discarded. Moreover, we propose to track the total privacy loss under the zero-concentrated DP (zCDP) and provide a generalization performance analysis. Experiments on real-world datasets demonstrate that under the same privacy guarantee, the proposed algorithms are superior to the state of the art in terms of model accuracy and convergence rate.

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Nonconvex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions recently. We design a family of stochastic proximal gradient methods by applying arbitrary sampling to solve the empirical risk minimization problem with a non-convex and non-smooth regularizer. These methods draw mini-batches of training examples according to an arbitrary probability distribution when computing stochastic gradients. A unified analytic approach is developed to examine the convergence and computational complexity of these methods, allowing us to compare the different sampling schemes. We show that the independent sampling scheme tends to improve performance over the commonly-used uniform sampling scheme. Our new analysis also derives a tighter bound on convergence speed for the uniform sampling than the best one available so far. Empirical evaluations demonstrate that the proposed algorithms converge faster than the state of the art.

Matrix completion methods can benefit from side information besides the partially observed matrix. The use of side features describing the row and column entities of a matrix has been shown to reduce the sample complexity for completing the matrix. We propose a novel sparse formulation that explicitly models the interaction between the row and column side features to approximate the matrix entries. Unlike early methods, this model does not require the low-rank condition on the model parameter matrix. We prove that when the side features can span the latent feature space of the matrix to be recovered, the number of observed entries needed for an exact recovery is $O(\log N)$ where $N$ is the size of the matrix. When the side features are corrupted latent features of the matrix with a small perturbation, our method can achieve an $\epsilon$-recovery with $O(\log N)$ sample complexity, and maintains a $\O(N^{3/2})$ rate similar to classfic methods with no side information. An efficient linearized Lagrangian algorithm is developed with a strong guarantee of convergence. Empirical results show that our approach outperforms three state-of-the-art methods both in simulations and on real world datasets.