Communication-Efficient Distributed Dual Coordinate Ascent (1409.1458v2)

Abstract: Communication remains the most significant bottleneck in the performance of distributed optimization algorithms for large-scale machine learning. In this paper, we propose a communication-efficient framework, CoCoA, that uses local computation in a primal-dual setting to dramatically reduce the amount of necessary communication. We provide a strong convergence rate analysis for this class of algorithms, as well as experiments on real-world distributed datasets with implementations in Spark. In our experiments, we find that as compared to state-of-the-art mini-batch versions of SGD and SDCA algorithms, CoCoA converges to the same .001-accurate solution quality on average 25x as quickly.

• The paper introduces the COCOA framework which significantly reduces communication overhead by balancing local computation and inter-node data exchange.
• The paper leverages a primal-dual formulation that preserves convergence rates, achieving a .001-accurate solution up to 25 times faster than state-of-the-art methods.
• The paper demonstrates practical effectiveness on real-world datasets and opens avenues for further exploration into communication-efficient optimization approaches.

Communication-Efficient Distributed Dual Coordinate Ascent

The paper presents a novel approach to addressing the significant communication bottlenecks in distributed optimization algorithms, particularly focusing on large-scale machine learning tasks. The key contribution is the introduction of the COCOA framework, which stands for "Communication-efficient Distributed Dual Coordinate Ascent." This framework capitalizes on a primal-dual setting to considerably reduce the communication overhead typically encountered in distributed systems, while retaining robust convergence properties.

Summary of Key Contributions

The authors highlight several critical contributions and findings in their work:

1. Flexible Trade-off Between Communication and Computation: COCOA provides a mechanism to steer the trade-off between local computation and communication, making it adaptable to various computational environments, from high-latency clusters to low-latency multi-core setups.
2. Primal-Dual Optimization: The framework leverages the primal-dual formulation of problems, enabling it to combine results from local computations without the need for intense communication among compute nodes.
3. Convergence Rate: A significant theoretical contribution of this paper is the convergence rate analysis provided for COCOA, demonstrating that it maintains the convergence rate of the local optimization method used, such as SDCA, with geometrically smooth losses.
4. Practical Performance: Empirical results on real-world distributed datasets show that COCOA achieves a .001-accurate solution quality up to 25 times faster on average compared to state-of-the-art mini-batch versions of SGD and SDCA.

Theoretical Insights

The convergence analysis extends the understanding of distributed optimization by removing data-dependent assumptions generally required by other methods. This broader applicability is critical for varied and large datasets encountered in real-world scenarios. The paper claims a linear convergence rate for the proposed framework, applicable to smooth loss functions, emphasizing the framework's efficiency in balancing the computational load and communication frequency.

Implications and Future Work

Practically, COCOA offers a significant advancement in solving large-scale regularized loss minimization problems, often encountered in signal processing and machine learning. The reduced communication requirement makes it particularly advantageous in distributed settings, where communication costs can be a major limiting factor.

Theoretically, the paper sets the stage for more exploration into communication-efficient optimization methods, possibly extending to non-smooth loss functions. Future work might include adapting the analysis for different types of loss functions or further integrating safe update techniques to allow for even more aggressive communication savings.

Conclusion

This paper provides a substantial contribution to the field of distributed machine learning by enhancing the efficiency of dual coordinate ascent methods. The COCOA framework's ability to significantly reduce communication without sacrificing convergence speed is poised to become an important tool for researchers and practitioners dealing with large-scale learning systems. This work paves the way for future studies to further explore and exploit the primal-dual structure for communication-efficient learning across other domains and loss functions.