Online prediction methods are typically presented as serial algorithms running on a single processor. However, in the age of web-scale prediction problems, it is increasingly common to encounter situations where a single processor cannot keep up with the high rate at which inputs arrive. In this work, we present the algorithm, a method of converting many serial gradient-based online prediction algorithms into distributed algorithms. We prove a regret bound for this method that is asymptotically optimal for smooth convex loss functions and stochastic inputs. Moreover, our analysis explicitly takes into account communication latencies between nodes in the distributed environment. We show how our method can be used to solve the closely-related distributed stochastic optimization problem, achieving an asymptotically linear speed-up over multiple processors. Finally, we demonstrate the merits of our approach on a web-scale online prediction problem.
@cite_5 address the distributed online learning problem, with a similar motivation to ours: trying to address the scalability problem of online learning algorithms which are inherently sequential. The main observation @cite_5 make is that in many cases, computing the gradient takes much longer than computing the update according to the online prediction algorithm. Therefore, they present a pipeline computational model. Each worker alternates between computing the gradient and computing the update rule. The different workers are synchronized such that no two workers perform an update simultaneously.
@cite_5
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Online learning algorithms have impressive convergence properties when it comes to risk minimization and convex games on very large problems. However, they are inherently sequential in their design which prevents them from taking advantage of modern multi-core architectures. In this paper we prove that online learning with delayed updates converges well, thereby facilitating parallel online learning.