The case for and against fixed step-size: Stochastic approximation algorithms in optimization and machine learning

arXiv — stat.MLWednesday, November 12, 2025 at 5:00:00 AM
The paper titled 'The case for and against fixed step-size: Stochastic approximation algorithms in optimization and machine learning' explores the implications of using a fixed step-size in stochastic approximation (SA) algorithms, which are increasingly relevant in fields like optimization and reinforcement learning. It defines a recursive relationship for the algorithm and establishes that under an ergodicity assumption on the Markov chain, the pair process is geometrically ergodic. The study also highlights that for various moments, the expected distance to the true solution diminishes at a rate dependent on the step-size, indicating that careful selection of this parameter is critical for effective convergence. These findings contribute to the broader discourse on algorithmic efficiency in machine learning, suggesting that the choice of step-size can significantly impact the performance and reliability of stochastic methods.
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