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math.OC2024
Convergence of Markov Chains for Constant Step-size Stochastic Gradient Descent with Separable Functions
David Shirokoff, Philip Zaleski
Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov…
math.NA2024
Algebraic Conditions for Stability in Runge-Kutta Methods and Their Certification via Semidefinite Programming
Austin Juhl, David Shirokoff
In this work, we present approaches to rigorously certify - and -stability in Runge-Kutta methods through the solution of convex feasibility problems defined by linear mat…