2020/12/07 by Anas Barakat, Barakat, A., Pascal Bianchi +5 · 2 citations
Computer Science · Engineering · Mathematics · #34A12 #60F99 #62L20 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Probability (math.PR) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2012.04002
openalex publication_date 2020/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a general stochastic optimization procedure is studied,\nunifying several variants of the stochastic gradient descent such as, among\nothers, the stochastic heavy ball method, the Stochastic Nesterov Accelerated\nGradient algorithm (S-NAG), and the widely used Adam algorithm. The algorithm\nis seen as a noisy Euler discretization of a non-autonomous ordinary\ndifferential equation, recently introduced by Belotto da Silva and Gazeau,\nwhich is analyzed in depth. Assuming that the objective function is non-convex\nand differentiable, the stability and the almost sure convergence of the\niterates to the set of critical points are established. A noteworthy special\ncase is the convergence proof of S-NAG in a non-convex setting. Under some\nassumptions, the convergence rate is provided under the form of a Central Limit\nTheorem. Finally, the non-convergence of the algorithm to undesired critical\npoints, such as local maxima or saddle points, is established. Here, the main\ningredient is a new avoidance of traps result for non-autonomous settings,\nwhich is of independent interest.\n