Continuous-time Models for Stochastic Optimization Algorithms
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We propose a new continuous-time formulation for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance reduced techniques. We exploit this continuous-time model, together with a simple Lyapunov analysis as well as tools from stochastic calculus, in order to derive convergence bounds for various types of non-convex functions. We contrast these bounds to their known equivalent in discrete-time as well as derive new bounds. Our model also includes SVRG, for which we derive a linear convergence rate for the class of weakly quasi-convex and quadratically growing functions.
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