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LQG Online Learning
Giorgio Gnecco1, Alberto Bemporad2, Marco Gori3
1DYSCO Research Unit, IMT School for Advanced Studies, Piazza S. Francesco, 19-55110 Lucca, Italy giorgio.gnecco@imtlucca.it.
Neural Computation
|June 1, 2017
Summary
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.
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.
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