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The Boundedness Conditions for Model-Free HDP( λ )
IEEE Transactions on Neural Networks and Learning Systems
|November 13, 2018
Summary
This study introduces Heuristic Dynamic Programming with eligibility traces (HDP(λ)), proving its stability and effectiveness. This enhanced approach learns from multiple future rewards, outperforming traditional methods in complex simulations.
Area of Science:
- Artificial Intelligence
- Machine Learning
- Control Theory
Background:
- Heuristic Dynamic Programming (HDP) is a model-free approach for reinforcement learning.
- Eligibility traces are effective in Q-learning but their use in HDP was limited.
- Previous stability proofs for HDP did not include the λ parameter.
Purpose of the Study:
- To analyze the stability of a model-free action-dependent Heuristic Dynamic Programming (HDP) approach with eligibility traces (HDP(λ)).
- To extend the Uniformly Ultimately Bounded (UUB) proof for HDP to include the λ parameter.
- To demonstrate the effectiveness of HDP(λ) through simulations.
Main Methods:
- Lyapunov stability analysis was used to prove the UUB property of HDP(λ).
- The stability of critic and actor neural networks, and learning rates was demonstrated.
- Three case studies involving a nonlinear system, an inverted pendulum, and a 3D maze navigation were conducted.
Main Results:
- The Uniformly Ultimately Bounded (UUB) property of HDP(λ) was proven under specific conditions.
- HDP(λ) demonstrated boundedness of estimated errors for neural networks and learning rates.
- Simulations showed HDP(λ) achieved competitive performance compared to HDP, TD(λ), and Q(λ) across various scenarios.
Conclusions:
- Eligibility traces are beneficial for HDP, enhancing its learning capabilities.
- HDP(λ) offers a stable and effective reinforcement learning solution.
- The proposed HDP(λ) method is a valuable contribution for complex control tasks.
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