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This study introduces a novel online learning framework using optimal control and machine learning. The method offers smoother parameter estimates than the Kalman filter, showing improved robustness to outliers.

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Area of Science:

  • Control Theory
  • Machine Learning
  • Statistical Signal Processing

Background:

  • Online learning from supervised examples is crucial for adaptive systems.
  • Classical methods like the Linear Quadratic Gaussian (LQG) problem provide a foundation.
  • Existing methods can be sensitive to outliers and lack robustness.

Purpose of the Study:

  • To develop a novel optimal control formulation for online supervised learning.
  • To investigate the relationship between this new framework and LQG control.
  • To enhance robustness and smoothness of parameter estimates in online learning.

Main Methods:

  • Combining optimal control theory with machine learning techniques.
  • Formulating and solving an optimal control problem for online learning with regularization.
  • Comparing the proposed method with the Kalman filter for parameter estimation.

Main Results:

  • The proposed algorithm provides closed-form optimal solutions for online learning.
  • The method demonstrates greater robustness to outliers compared to the Kalman filter due to regularization.
  • Smoother time-varying parameter estimates are achieved.

Conclusions:

  • The developed optimal control framework offers a robust and efficient approach to online supervised learning.
  • Regularization is key to improving outlier resilience and estimate smoothness.
  • Extensions to infinite horizons and nonlinear models are feasible.