Distributed Optimization with Arbitrary Local Solvers (1512.04039v2)

Abstract: With the growth of data and necessity for distributed optimization methods, solvers that work well on a single machine must be re-designed to leverage distributed computation. Recent work in this area has been limited by focusing heavily on developing highly specific methods for the distributed environment. These special-purpose methods are often unable to fully leverage the competitive performance of their well-tuned and customized single machine counterparts. Further, they are unable to easily integrate improvements that continue to be made to single machine methods. To this end, we present a framework for distributed optimization that both allows the flexibility of arbitrary solvers to be used on each (single) machine locally, and yet maintains competitive performance against other state-of-the-art special-purpose distributed methods. We give strong primal-dual convergence rate guarantees for our framework that hold for arbitrary local solvers. We demonstrate the impact of local solver selection both theoretically and in an extensive experimental comparison. Finally, we provide thorough implementation details for our framework, highlighting areas for practical performance gains.

• The paper introduces a novel distributed optimization framework that allows arbitrary local solvers and provides strong primal-dual convergence rate guarantees.
• The framework promotes reusability of existing solver optimizations and includes mechanisms to balance communication and computation efficiently across different system types.
• Extensive experiments demonstrate that the framework achieves robust scaling and often surpasses the efficiency of highly specific distributed solvers on large-scale datasets.

Distributed Optimization with Arbitrary Local Solvers

The paper introduces a novel framework for distributed optimization, addressing the challenges posed by the extensive data sizes that necessitate computation beyond the confines of a single machine. As datasets grow larger, traditional single-machine solvers, despite their impressive capabilities, need adaptation to leverage distributed resources effectively. The authors present an innovative framework that adapts these well-tuned single-machine solvers for distributed environments without losing their competitive edge.

The proposed framework distinguishes itself by allowing the use of arbitrary local solvers on each machine, offering a significant degree of flexibility and ease of integration with existing algorithms. A key aspect of this framework is its ability to provide strong primal-dual convergence rate guarantees applicable to any local solvers used. This flexibility is instrumental in translating the advancements and specific tunings of single-machine solvers into the distributed computing sphere, thus facilitating performance enhancements as methods evolve over time.

Key Contributions

1. Arbitrary Local Solvers: The framework enables the utilization of any local solver on each distributed machine, promoting reusability while maintaining flexibility. This feature allows practitioners to leverage existing solver optimizations targeted at particular problem instances without redesigning for distributed contexts.
2. Communication Efficiency: The framework addresses the critical communications bottleneck in distributed settings. By decoupling communication from computation, and balancing these two through adjustable parameters, the framework flexes to cater to various communication speeds, from high-performance computing setups to slower distributed systems like Hadoop.
3. Theoretical Underpinnings: The authors extend and reinforce current methods like CoCoA, offering enhanced theoretical convergence for both smooth and non-smooth losses. Particularly noteworthy is their strong theoretical guarantee, unaffected by the number of machines as data size remains constant.
4. Practical Performance: The paper provides extensive computational performance demonstrations. Experiments underline how the CoCoA+ framework not only maintains but often surpasses the efficiency of highly specific distributed solvers, especially on large-scale datasets. Performance gains from improved local solvers automatically translate throughout the distributed system.

Results and Implications

The experimental results validate the framework's efficiency and adaptability, showing that solver performance scales favorably with data size and machine number. A notable finding is the robust scaling of the framework, retaining efficiency as more machines are included and data remains unchanged in size.

Further, the approach improves upon existing distributed methods by allowing stronger scaling and faster convergence, particularly with enhanced support for smooth and non-smooth losses. This positions the CoCoA+ framework as a versatile tool for distributed machine learning, promising continued relevance as more sophisticated local solvers develop.

Future Directions

The paper opens several avenues for further research. The implications of flexibility in choosing local solvers suggest exploring other solver types and further fine-tuning communication-computation balance based on specific distributed hardware characteristics. There is also potential in investigating how the framework can integrate seamlessly with evolving machine learning models that inherently support distributed training, such as deep learning architectures.

Overall, the paper offers a comprehensive framework that not only addresses current challenges in distributed optimization but establishes a foundational approach adaptable to future computational landscapes in machine learning.