2021/11/10 by Gregory Schwartzman, Schwartzman, Gregory
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2111.05478
openalex publication_date 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that stochastic gradient descent (SGD) finds a solution that achieves (1-ε) classification accuracy on the entire dataset. We do so under two main assumptions: (1. Local progress) The model accuracy improves on average over batches. (2. Models compute simple functions) The function computed by the model is simple (has low Kolmogorov complexity). It is sufficient that these assumptions hold only for a tiny fraction of the epochs. Intuitively, the above means that intermittent local progress of SGD implies global progress. Assumption 2 trivially holds for underparameterized models, hence, our work gives the first convergence guarantee for general, underparameterized models. Furthermore, this is the first result which is completely model agnostic - we do not require the model to have any specific architecture or activation function, it may not even be a neural network. Our analysis makes use of the entropy compression method, which was first introduced by Moser and Tardos in the context of the Lovász local lemma.