GIANT: Globally Improved Approximate Newton Method for Distributed Optimization
This work addresses communication bottlenecks in distributed optimization for machine learning, offering a practical solution with fewer tuning parameters, though it is incremental as it builds on existing Newton-type methods.
The authors tackled the problem of distributed empirical risk minimization by proposing GIANT, a communication-efficient Newton-type method that reduces communication rounds through local computations, achieving an improved convergence rate compared to first-order and existing distributed Newton methods. Empirically, GIANT demonstrated superior performance in large-scale experiments on a computer cluster.
For distributed computing environment, we consider the empirical risk minimization problem and propose a distributed and communication-efficient Newton-type optimization method. At every iteration, each worker locally finds an Approximate NewTon (ANT) direction, which is sent to the main driver. The main driver, then, averages all the ANT directions received from workers to form a {\it Globally Improved ANT} (GIANT) direction. GIANT is highly communication efficient and naturally exploits the trade-offs between local computations and global communications in that more local computations result in fewer overall rounds of communications. Theoretically, we show that GIANT enjoys an improved convergence rate as compared with first-order methods and existing distributed Newton-type methods. Further, and in sharp contrast with many existing distributed Newton-type methods, as well as popular first-order methods, a highly advantageous practical feature of GIANT is that it only involves one tuning parameter. We conduct large-scale experiments on a computer cluster and, empirically, demonstrate the superior performance of GIANT.