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On Gradient-Based Optimization: Accelerated, Stochastic and Nonconvex

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STSW01 - Theoretical and algorithmic underpinnings of Big Data

Many new theoretical challenges have arisen in the area of gradient-based optimization for large-scale statistical data analysis, driven by the needs of applications and the opportunities provided by new hardware and software platforms. I discuss several related, recent results in this area: (1) a new framework for understanding Nesterov acceleration, obtained by taking a continuous-time, Lagrangian/Hamiltonian/symplectic perspective, (2) a discussion of how to escape saddle points efficiently in nonconvex optimization, and (3) the acceleration of Langevin diffusion.

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