Control Policy Optimization with Quasi-Newton Trust Regions
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Solution Overview
Problem
Current policy gradient algorithms in Reinforcement Learning face challenges in achieving monotonic improvement and efficient sample usage, particularly in physical systems, due to difficulties in selecting optimal learning rates and incorporating curvature information for trust region optimization.
Innovation Solution
The implementation of a Quasi-Newton Trust Region Method (QNTPM) for policy optimization, which uses the BFGS method to compute the Hessian of the objective function and the Dogleg method to determine steps within a trust region, iteratively updating the trust region radius based on the quadratic model's approximation accuracy, and employing a limited-memory Quasi-Newton approximation to estimate the Hessian.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If gradient descent methods are used for policy optimization, then the algorithm is simple to implement, but monotonic improvement of policy performance cannot be ensured
Solution Approach 1:
The patent introduces a trust region as an intermediary mechanism between the gradient descent algorithm and the policy optimization process. By constraining updates to occur within a trust region where the quadratic model is valid, the method ensures monotonic improvement while maintaining the simplicity of gradient-based approaches. The trust region acts as a mediator that guarantees performance improvement without requiring complex algorithms.
2Reliability
If a trust region algorithm is used for policy optimization, then monotonic improvement is ensured, but the algorithm complexity increases
Solution Approach 1:
The patent uses a quadratic model as a cheap, simplified representation of the objective function within the trust region. This quadratic approximation is computationally inexpensive to evaluate and update, allowing the algorithm to perform multiple iterations within the trust region without excessive computational cost. The quadratic model serves as a disposable approximation that is discarded and rebuilt in each iteration.
3Measurement precision
If the trust region radius is kept small to ensure model accuracy, then the quadratic model approximation is reliable, but the convergence speed decreases
Solution Approach 1:
The patent implements a dynamic trust region radius that adapts based on the agreement between the quadratic model predictions and actual objective function evaluations. When the model accurately predicts improvements, the trust region radius is expanded to allow larger steps and faster convergence. When predictions are inaccurate, the radius is contracted to maintain reliability. This dynamic adjustment resolves the contradiction between model accuracy and convergence speed.
4Speed
If the trust region radius is increased to speed up convergence, then the algorithm converges faster, but the quadratic model approximation becomes less accurate
Solution Approach 1:
The patent employs feedback mechanisms where the actual performance improvement from policy updates is compared against the predicted improvement from the quadratic model. This feedback is used to adjust the trust region radius for subsequent iterations. If the actual improvement matches or exceeds predictions, the trust region is expanded; if not, it is contracted. This feedback loop ensures the trust region radius is always appropriate for the current model accuracy.
Data Source
AI summary
A computer-implemented learning method for optimizing a control policy controlling a system is provided. The method includes receiving states of the system being operated for a specific task, initializing the control policy as a function approximator including neural networks, collecting state transition and reward data using a current control policy, estimating an advantage function and a state visitation frequency based on the current control policy, updating the current control policy using the second-order approximation of the objective function, a second-order approximation of the KL-divergence constraint on the permissible change in the policy using a quasi-newton trust region policy optimization, and determining an optimal control policy, for controlling the system, based on the average reward accumulated using the updated current control policy.