Towards Continuous-Time Approximations for Stochastic Gradient Descent without Replacement

arXiv — cs.LGFriday, December 5, 2025 at 5:00:00 AM
  • A new study presents a stochastic, continuous-time approximation for stochastic gradient descent without replacement (SGDo), utilizing a Young differential equation driven by an 'epoched Brownian motion'. This method addresses the underexplored mathematical theory of SGDo compared to its counterparts, proving almost sure convergence for strongly convex objectives and specific learning rate schedules.
  • The development is significant as it enhances the theoretical understanding of SGDo, which is widely used in training machine learning models. By providing a robust mathematical framework, it may lead to more efficient optimization algorithms in practical applications.
  • This advancement reflects ongoing efforts in the field of machine learning to refine optimization techniques, particularly in handling noisy and irregular objective functions. The exploration of gradient-free optimization methods and their convergence properties indicates a broader trend towards improving algorithmic efficiency and reliability in various applications.
— via World Pulse Now AI Editorial System

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