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Kunal Menda*, Jean de Becdelièvre*, Jayesh K. Gupta*,
Ilan Kroo, Mykel J. Kochenderfer, and Zachary Manchester
Stanford University
System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent approximation to expectation-maximization can be a reliable and scalable approach for high-dimensional deterministic systems, as often encountered in robotics. We formulate certainty-equivalent expectation-maximization as block coordinate-ascent, and detail an efficient implementation. We test the algorithm on a simulated system of coupled Lorenz attractors, showing its ability to identify high-dimensional systems that can be intractable for particle-based approaches. We also identify the dynamics of an aerobatic helicopter. By augmenting the state with unobserved fluid states, a model is learned that predicts the acceleration of the helicopter better than state-of-the-art approaches.
Overview
Overview
Standard Approach: Particle EM
Our Approach: CE-EM
CE-EM
CE-EM
Find x and θ using Block-Coordinate Descent
Results
Results
- Bias-variance Tradeoff
CE-EM usually converges to local optima with low variance.
However with large process noise, it can lead to small bias.
Single Lorenz Attractor
2. Performance
2. Performance
CE-EM converges in order of magnitude fewer epochs, while being 47x faster than Particle-EM per epoch.
Coupled Lorenz Attractors
3. Convergence in High-dimensional Problems
3. Convergence in High-dimensional Problems
CE-EM shows monotonic convergence to local optima while Particle EM converges to poor parameter estimates.
4. Scalability to Real-world High-dimensional Problems
4. Scalability to Real-world High-dimensional Problems
CE-EM allows training non-linear neural network models to achieve best accuracy.
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