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Least squares solutions of the HJB equation with neural network value-function approximators
1The Interdisciplinary Center for Neural Computation, The Hebrew University, Jerusalem 91904, Israel. tassa@alice.nc.huji.ac.il
IEEE Transactions on Neural Networks
|August 3, 2007
Summary
This study introduces novel methods for solving optimal control problems using neural networks to approximate value functions. The techniques improve convergence for complex systems like the inverted pendulum.
Area of Science:
- Optimal Control
- Machine Learning
- Applied Mathematics
Background:
- Solving Hamilton-Jacobi-Bellman (HJB) equations is crucial for optimal control.
- Neural networks (NNs) offer a powerful tool for approximating value functions in complex systems.
- Numerical instabilities can arise from nonlinearities in optimal control problems and NN approximations.
Purpose of the Study:
- To present an empirical study of iterative least squares minimization of the HJB residual using NN value function approximation.
- To introduce and validate two methods for promoting convergence in these complex optimal control problems.
- To demonstrate the effectiveness of the proposed methods on challenging control tasks.
Main Methods:
- Iterative least squares minimization of the HJB residual.
- Employing neural networks for value function approximation.
- Two proposed convergence-promoting methods: gradual horizon time scaling and assuming stochastic dynamics for regularization.
Main Results:
- Demonstrated effective convergence for optimal control problems with NN approximations.
- Successfully solved complex problems, including a 4-D inverted-pendulum system with bounded control.
- Validated the effectiveness of gradual horizon time scaling and stochastic dynamics regularization for stabilization.
Conclusions:
- The proposed methods offer a practical approach to solving optimal control problems without requiring initial stabilizing policies or restrictive assumptions.
- Knowledge of plant dynamics is sufficient for applying this method.
- The study provides equations for differential backpropagation, aiding implementation.
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