DINGO: Distributed Newton-Type Method for Gradient-Norm Optimization
This addresses communication efficiency in distributed optimization for machine learning and data science, but appears incremental as it builds on existing Newton-type methods like Newton-MR.
The paper tackles the problem of optimizing a sum of functions in distributed computing by proposing DINGO, a communication-efficient Newton-type algorithm that guarantees a strict reduction in gradient norm regardless of hyper-parameter choices, with empirical evidence showing effectiveness, stability, and versatility.
For optimization of a sum of functions in a distributed computing environment, we present a novel communication efficient Newton-type algorithm that enjoys a variety of advantages over similar existing methods. Similar to Newton-MR, our algorithm, DINGO, is derived by optimization of the gradient's norm as a surrogate function. DINGO does not impose any specific form on the underlying functions, and its application range extends far beyond convexity. In addition, the distribution of the data across the computing environment can be arbitrary. Further, the underlying sub-problems of DINGO are simple linear least-squares, for which a plethora of efficient algorithms exist. Lastly, DINGO involves a few hyper-parameters that are easy to tune. Moreover, we theoretically show that DINGO is not sensitive to the choice of its hyper-parameters in that a strict reduction in the gradient norm is guaranteed, regardless of the selected hyper-parameters. We demonstrate empirical evidence of the effectiveness, stability and versatility of our method compared to other relevant algorithms.