Publication

Diffusion Learning In Non-Convex Environments

Ali H. Sayed, Stefan Vlaski
2019
Conference Papers

Abstract

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, recent years have seen rising interest in the behavior of gradient-descent based algorithms in non-convex environments. Most of the works on distributed non-convex optimization focus on the deterministic setting, where exact gradients are available at each agent. In this work, we consider stochastic cost functions, where exact gradients are replaced by stochastic approximations and the resulting gradient noise persistently seeps into the dynamics of the algorithm. We establish that the diffusion algorithm continues to yield meaningful estimates in these more challenging, non-convex environments, in the sense that (a) despite the distributed implementation, restricted to local interactions, individual agents cluster in a small region around a common and well-defined vector, which will carry the interpretation of a network centroid, and (b) the network centroid inherits many properties of the centralized, stochastic gradient descent recursion, including the return of an O(mu)-mean-square-stationary point in at most O(1/mu(2)) iterations.

Official source

https://infoscience.epfl.ch/entities/publication/f7de1f72-4925-4db3-ad9f-1b7efef6da0a

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Ali H. Sayed, Stefan Vlaski
2019
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/f7de1f72-4925-4db3-ad9f-1b7efef6da0a

About this result

Related concepts (30)

Stochastic gradient descent

Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient (calculated from the entire data set) by an estimate thereof (calculated from a randomly selected subset of the data).

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In computer science, online machine learning is a method of machine learning in which data becomes available in a sequential order and is used to update the best predictor for future data at each step, as opposed to batch learning techniques which generate the best predictor by learning on the entire training data set at once. Online learning is a common technique used in areas of machine learning where it is computationally infeasible to train over the entire dataset, requiring the need of out-of-core algorithms.

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