Empirical Risk Minimization and Stochastic Gradient Descent for Relational Data

Veitch, Victor; Austern, Morgane; Zhou, Wenda; Blei, David M.; Orbanz, Peter

doi:10.48550/arxiv.1806.10701

Cited by 1 publication

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“…is characterised by a data sample y i . Such problems naturally arise in various applications in the machine learning area, such as classification, regression, pattern recognition, image processing, bio-informatics and social networks [13]- [16]. Moreover, these optimization problems are typically huge and need to be solved efficiently.…”

Section: Introductionmentioning

confidence: 99%

Parallel Stochastic Optimization Framework for Large-Scale Non-Convex Stochastic Problems

Omidvar,

Liu,

Lau

et al. 2019

Preprint

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In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed is critical for many emerging applications, most existing stochastic optimization methods suffer from slow convergence. Furthermore, the emerging technology of parallel computing has motivated an increasing demand for designing new stochastic optimization schemes that can handle parallel optimization for implementation in distributed systems.We propose a fast parallel stochastic optimization framework that can solve a large class of possibly non-convex stochastic optimization problems that may arise in applications with multi-agent systems. In the proposed method, each agent updates its control variable in parallel, by solving a convex quadratic subproblem independently. The convergence of the proposed method to the optimal solution for convex problems and to a stationary point for general non-convex problems is established.The proposed algorithm can be applied to solve a large class of optimization problems arising in important applications from various fields, such as machine learning and wireless networks. As a representative application of our proposed stochastic optimization framework, we focus on large-scale support vector machines and demonstrate how our algorithm can efficiently solve this problem, especially in modern applications with huge datasets. Using popular real-world datasets, we present experimental results to demonstrate the merits of our proposed framework by comparing its performance to the state-of-the-art in the literature. Numerical results show that the proposed method can significantly outperform the state-of-the-art methods in terms of the convergence speed while having the same or lower complexity and storage requirement.

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Section: Introductionmentioning

confidence: 99%