A Rate Transfer Method: Convergence Rates in Stochastic Gradient Descent via Stochastic Calculus
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Abstract (arXiv)
We develop a rate-transfer method that converts finite-time Lyapunov estimates for an associated stochastic differential equation (SDE) into finite-time convergence bounds for stochastic gradient algorithms. Under generic moment and smoothness conditions, the convergence analysis of the stochastic gradient method reduces to a calculus argument verifying a Lyapunov generator inequality for the SDE. The method recovers established rates for classical stochastic gradient methods and provides a way to establish convergence rates for new optimization algorithms through calculus arguments applied to their associated SDEs.
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References · 5
- 2015Stochastic modified equations and adaptive stochastic gradient algorithmscited by 142
- 2018Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundationscited by 114
- 2018Continuous-time Models for Stochastic Optimization Algorithmscited by 17
- 2019Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximationcited by 15
- 2022On uniform-in-time diffusion approximation for stochastic gradient descentcited by 6
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