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1.	Berglund, Erik, et al. (author) Distributed Newton Method Over Graphs : Can Sharing of Second-Order Information Eliminate the Condition Number Dependence? 2021 In: IEEE Signal Processing Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 1070-9908 .- 1558-2361. ; 28, s. 1180-1184 Journal article (peer-reviewed)abstract One of the main advantages of second-order methods in a centralized setting is that they are insensitive to the condition number of the objective function's Hessian. For applications such as regression analysis, this means that less pre-processing of the data is required for the algorithm to work well, as the ill-conditioning caused by highly correlated variables will not be as problematic. Similar condition number independence has not yet been established for distributed methods. In this paper, we analyze the performance of a simple distributed second-order algorithm on quadratic problems and show that its convergence depends only logarithmically on the condition number. Our empirical results indicate that the use of second-order information can yield large efficiency improvements over first-order methods, both in terms of iterations and communications, when the condition number is of the same order of magnitude as the problem dimension.

Berglund, Erik, et al. (author)
Distributed Newton Method Over Graphs : Can Sharing of Second-Order Information Eliminate the Condition Number Dependence?
2021
In: IEEE Signal Processing Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 1070-9908 .- 1558-2361. ; 28, s. 1180-1184
Journal article (peer-reviewed)abstract
- One of the main advantages of second-order methods in a centralized setting is that they are insensitive to the condition number of the objective function's Hessian. For applications such as regression analysis, this means that less pre-processing of the data is required for the algorithm to work well, as the ill-conditioning caused by highly correlated variables will not be as problematic. Similar condition number independence has not yet been established for distributed methods. In this paper, we analyze the performance of a simple distributed second-order algorithm on quadratic problems and show that its convergence depends only logarithmically on the condition number. Our empirical results indicate that the use of second-order information can yield large efficiency improvements over first-order methods, both in terms of iterations and communications, when the condition number is of the same order of magnitude as the problem dimension.

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