- The paper introduces DANE, a novel algorithm reducing communication rounds by approximating the Hessian inverse for quadratic objectives.
- It employs a method that alternates between local optimization and global communication to streamline distributed parameter updates.
- Empirical results demonstrate that DANE outperforms ADMM and one-shot averaging, making it effective for large-scale machine learning.
Communication Efficient Distributed Optimization using an Approximate Newton-type Method
The paper introduces a novel approach to distributed optimization focusing on an approximate Newton-type method, termed DANE (Distributed Approximate NEwton). This method is well-suited for stochastic optimization and learning tasks, leveraging improvements in convergence rates through the efficient use of communication between distributed machines.
Theoretical Insights
The authors address the optimization problem where multiple machines possess local functions, and the objective is to minimize their average. The method excels particularly in quadratic objectives, demonstrating linear convergence rates that improve with larger datasets. Under reasonable assumptions, DANE achieves a rate that is essentially independent of the sample size by minimizing the empirical objective using a minimal number of iterations.
The authors provide a detailed analysis contrasting DANE with existing approaches like one-shot parameter averaging and ADMM. This analysis reveals that DANE outperforms these methods in scenarios where dataset size grows, offering a significant reduction in required communication rounds, a critical factor in distributed systems where communication costs are high.
Methodology
DANE's core mechanism involves alternating between local optimization at each machine and a communication round using map-reduce operations. The method is positioned as an approximate Newton-type strategy, where at each iteration, local machines solve sub-problems grounded on their local data while approximating the global objective's geometry.
Crucially, the paper establishes that for quadratic objectives, DANE can replace the true Hessian inverse in Newton's method with an average inverse of approximate Hessians, significantly reducing computational overhead without needing explicit Hessians. Through this, DANE achieves a form of implicit regularization, facilitating quick convergence to the global objective's minimizer.
Empirical Evidence
The authors support their theoretical claims with empirical results, indicating that DANE outpaces ADMM, especially when scaling with the increased datasets distributed across machines. Real-world datasets and synthetic experiments corroborate the method's efficiency, notably in stochastic quadratic scenarios where individualized steps per local machine further reduce computational burden and iterations required for convergence.
Implications and Future Directions
The implications of the proposed method span both theoretical and practical dimensions. Theoretically, DANE enhances the understanding of distributed optimization, specifically the role of Newton-type methods in reducing communication inefficiencies. Practically, this methodology promises improvements in machine learning settings where large data volumes are split across distributed architectures, such as large-scale training of models in cloud environments.
Future research may investigate further optimization classes beyond quadratics and assess DANE's adaptability to non-convex objectives. Its performance in non-quadratic settings, as hinted by preliminary analysis, suggests potential adaptations or extensions that could solidify its applicability in broader machine learning contexts. Additionally, fine-tuning hyperparameters like regularization and step sizes in practice remains an area ripe for exploration.
Conclusion
This paper contributes significantly to distributed optimization by proposing a Newton-type method that economizes communication without sacrificing convergence speed. DANE stands out for its adaptability to distributed systems and provides a compelling foundation for future studies aiming at scalable, efficient optimization techniques in machine learning and parallel computing tasks.