2024/05/24 by Alexander Tyurin, Tyurin, Alexander, Kaja Gruntkowska +3 · 2 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Complexity and Algorithms in Graphs #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2405.15545
openalex publication_date 2024/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In practical distributed systems, workers are typically not homogeneous, and due to differences in hardware configurations and network conditions, can have highly varying processing times. We consider smooth nonconvex finite-sum (empirical risk minimization) problems in this setup and introduce a new parallel method, Freya PAGE, designed to handle arbitrarily heterogeneous and asynchronous computations. By being robust to "stragglers" and adaptively ignoring slow computations, Freya PAGE offers significantly improved time complexity guarantees compared to all previous methods, including Asynchronous SGD, Rennala SGD, SPIDER, and PAGE, while requiring weaker assumptions. The algorithm relies on novel generic stochastic gradient collection strategies with theoretical guarantees that can be of interest on their own, and may be used in the design of future optimization methods. Furthermore, we establish a lower bound for smooth nonconvex finite-sum problems in the asynchronous setup, providing a fundamental time complexity limit. This lower bound is tight and demonstrates the optimality of Freya PAGE in the large-scale regime, i.e., when √(m) ≥ n, where n is # of workers, and m is # of data samples.