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This study optimizes distributed regression communication complexity using randomized methods. New bounds significantly improve upon prior work for both least squares and general regression problems.

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Area of Science:

  • Distributed computing
  • Information theory
  • Machine learning

Background:

  • The distributed regression problem involves a coordinator and multiple servers holding data partitions.
  • Existing communication complexity bounds for this problem are suboptimal, particularly for general regression.

Purpose of the Study:

  • To derive improved randomized communication complexity bounds for the distributed regression problem in the coordinator model.
  • To establish optimal bounds for least squares regression and provide new bounds for general regression.

Main Methods:

  • Utilizing a randomized approach within the coordinator model for distributed computation.
  • Analyzing communication complexity in the arbitrary partition model where data is additively shared.

Main Results:

  • Achieved the first optimal bound of O(log(1/δ)) bits for distributed least squares regression.
  • Established an O(n^(1/3)) upper bound for general distributed regression.
  • Demonstrated that for large n, the leading term depends linearly, not quadratically, on n.
  • Proved communication lower bounds of Ω(n^(1/3)) for general regression and Ω(1) for least squares.

Conclusions:

  • The new bounds represent significant improvements over existing results.
  • The findings offer more efficient communication protocols for distributed regression tasks.