No Arabic abstract
This paper targets solving distributed machine learning problems such as federated learning in a communication-efficient fashion. A class of new stochastic gradient descent (SGD) approaches have been developed, which can be viewed as the stochastic generalization to the recently developed lazily aggregated gradient (LAG) method --- justifying the name LASG. LAG adaptively predicts the contribution of each round of communication and chooses only the significant ones to perform. It saves communication while also maintains the rate of convergence. However, LAG only works with deterministic gradients, and applying it to stochastic gradients yields poor performance. The key components of LASG are a set of new rules tailored for stochastic gradients that can be implemented either to save download, upload, or both. The new algorithms adaptively choose between fresh and stale stochastic gradients and have convergence rates comparable to the original SGD. LASG achieves impressive empirical performance --- it typically saves total communication by an order of magnitude.
In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed controllers can be learned with sub-linear sample complexity and computed with near-linear time complexity, both measured with respect to the dimension of the system. In particular, we provide sharp end-to-end guarantees on the stability and the performance of the designed distributed controller and prove that for sparse systems, the number of samples needed to guarantee robust and near optimal performance of the designed controller can be significantly smaller than the dimension of the system. Finally, we show that the proposed optimization problem can be solved to global optimality with near-linear time complexity by iteratively solving a series of small quadratic programs.
We introduce a collaborative learning framework allowing multiple parties having different sets of attributes about the same user to jointly build models without exposing their raw data or model parameters. In particular, we propose a Federated Stochastic Block Coordinate Descent (FedBCD) algorithm, in which each party conducts multiple local updates before each communication to effectively reduce the number of communication rounds among parties, a principal bottleneck for collaborative learning problems. We analyze theoretically the impact of the number of local updates and show that when the batch size, sample size, and the local iterations are selected appropriately, within $T$ iterations, the algorithm performs $mathcal{O}(sqrt{T})$ communication rounds and achieves some $mathcal{O}(1/sqrt{T})$ accuracy (measured by the average of the gradient norm squared). The approach is supported by our empirical evaluations on a variety of tasks and datasets, demonstrating advantages over stochastic gradient descent (SGD) approaches.
In this paper, we study distributed algorithms for large-scale AUC maximization with a deep neural network as a predictive model. Although distributed learning techniques have been investigated extensively in deep learning, they are not directly applicable to stochastic AUC maximization with deep neural networks due to its striking differences from standard loss minimization problems (e.g., cross-entropy). Towards addressing this challenge, we propose and analyze a communication-efficient distributed optimization algorithm based on a {it non-convex concave} reformulation of the AUC maximization, in which the communication of both the primal variable and the dual variable between each worker and the parameter server only occurs after multiple steps of gradient-based updates in each worker. Compared with the naive parallel version of an existing algorithm that computes stochastic gradients at individual machines and averages them for updating the model parameters, our algorithm requires a much less number of communication rounds and still achieves a linear speedup in theory. To the best of our knowledge, this is the textbf{first} work that solves the {it non-convex concave min-max} problem for AUC maximization with deep neural networks in a communication-efficient distributed manner while still maintaining the linear speedup property in theory. Our experiments on several benchmark datasets show the effectiveness of our algorithm and also confirm our theory.
We study distributed stochastic gradient (D-SG) method and its accelerated variant (D-ASG) for solving decentralized strongly convex stochastic optimization problems where the objective function is distributed over several computational units, lying on a fixed but arbitrary connected communication graph, subject to local communication constraints where noisy estimates of the gradients are available. We develop a framework which allows to choose the stepsize and the momentum parameters of these algorithms in a way to optimize performance by systematically trading off the bias, variance, robustness to gradient noise and dependence to network effects. When gradients do not contain noise, we also prove that distributed accelerated methods can emph{achieve acceleration}, requiring $mathcal{O}(kappa log(1/varepsilon))$ gradient evaluations and $mathcal{O}(kappa log(1/varepsilon))$ communications to converge to the same fixed point with the non-accelerated variant where $kappa$ is the condition number and $varepsilon$ is the target accuracy. To our knowledge, this is the first acceleration result where the iteration complexity scales with the square root of the condition number in the context of emph{primal} distributed inexact first-order methods. For quadratic functions, we also provide finer performance bounds that are tight with respect to bias and variance terms. Finally, we study a multistage version of D-ASG with parameters carefully varied over stages to ensure exact $mathcal{O}(-k/sqrt{kappa})$ linear decay in the bias term as well as optimal $mathcal{O}(sigma^2/k)$ in the variance term. We illustrate through numerical experiments that our approach results in practical algorithms that are robust to gradient noise and that can outperform existing methods.
We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of bits. Most previous communication-efficient approaches for this problem are limited to first-order optimization, and therefore have emph{linear} dependence on the condition number in their communication complexity. We show that this dependence is not inherent: communication-efficient methods can in fact have sublinear dependence on the condition number. For this, we design and analyze the first communication-efficient distributed variants of preconditioned gradient descent for Generalized Linear Models, and for Newtons method. Our results rely on a new technique for quantizing both the preconditioner and the descent direction at each step of the algorithms, while controlling their convergence rate. We also validate our findings experimentally, showing fast convergence and reduced communication.