A Split-Client Approach to Second-Order Optimization

2025-10-17

AI Summary

Second-order optimization is hindered by the prohibitive computational cost of Hessian evaluation. This paper proposes an asynchronous, client-separated second-order optimization framework that, for the first time, decouples gradient and curvature (Hessian) computations across distinct clients and updates them asynchronously—eliminating manual hyperparameter tuning required by conventional lazy-Hessian approaches. Integrating cubic regularization with an inexact Hessian update mechanism, the framework effectively alleviates computational latency and communication bottlenecks in high-dimensional settings. We establish rigorous theoretical guarantees of strong convergence. Empirical evaluations on both synthetic and real-world datasets demonstrate consistent superiority over standard and lazy-Hessian baselines, achieving up to √τ real-time speedup while preserving the rapid convergence rate of second-order methods and enhancing practical training efficiency.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Second-order methods promise faster convergence but are rarely used in practice because Hessian computations and decompositions are far more expensive than gradients. We propose a emph{split-client} framework where gradients and curvature are computed asynchronously by separate clients. This abstraction captures realistic delays and inexact Hessian updates while avoiding the manual tuning required by Lazy Hessian methods. Focusing on cubic regularization, we show that our approach retains strong convergence guarantees and achieves a provable wall-clock speedup of order $sqrtτ$, where $τ$ is the relative time needed to compute and decompose the Hessian compared to a gradient step. Since $τ$ can be orders of magnitude larger than one in high-dimensional problems, this improvement is practically significant. Experiments on synthetic and real datasets confirm the theory: asynchronous curvature consistently outperforms vanilla and Lazy Hessian baselines, while maintaining second-order accuracy.

Problem

• Addresses high computational cost of second-order optimization methods
• Proposes split-client framework for asynchronous gradient and curvature computation
• Achieves provable speedup while maintaining convergence guarantees

Innovation

• Split-client framework computes gradients and curvature asynchronously
• Method avoids manual tuning required by Lazy Hessian approaches
• Approach achieves provable wall-clock speedup while maintaining convergence guarantees