  Distributed stochastic optimization methods based on Newton's method offer
significant advantages over first-order methods by leveraging curvature
information for improved performance. However, the practical applicability of
Newton's method is hindered in large-scale and heterogeneous learning
environments due to challenges such as high computation and communication costs
associated with the Hessian matrix, sub-model diversity, staleness in training,
and data heterogeneity. To address these challenges, this paper introduces a
novel and efficient algorithm called RANL, which overcomes the limitations of
Newton's method by employing a simple Hessian initialization and adaptive
assignments of training regions. The algorithm demonstrates impressive
convergence properties, which are rigorously analyzed under standard
assumptions in stochastic optimization. The theoretical analysis establishes
that RANL achieves a linear convergence rate while effectively adapting to
available resources and maintaining high efficiency. Unlike traditional
first-order methods, RANL exhibits remarkable independence from the condition
number of the problem and eliminates the need for complex parameter tuning.
These advantages make RANL a promising approach for distributed stochastic
optimization in practical scenarios.
