arXiv:2403.16825v2 Announce Type: replace Abstract: We prove that a single-layer neural network trained with the online actor critic algorithm converges in distribution to a random ordinary differential equation (ODE) as the number of hidden units and the number of training steps $\rightarrow \infty$. In the online actor-critic algorithm, the distribution of the data samples dynamically changes as the model is updated, which is a key challenge for any convergence analysis. We establish the geometric ergodicity of the data samples under a fixed actor policy. Then, using a Poisson equation, we p
This research is part of ongoing efforts in AI theory to establish rigorous mathematical foundations for deep learning algorithms, a critical step as AI systems become more complex and integrated into real-world applications.
Understanding the convergence properties of online neural actor-critic methods provides theoretical guarantees for reinforcement learning algorithms, which are vital for building reliable and predictable autonomous systems.
This theoretical work helps bridge the gap between empirical success and mathematical understanding in reinforcement learning, offering a foundation for designing more robust and efficient AI training processes.
- · AI researchers
- · Reinforcement learning applications
- · Autonomous system developers
- · Empirical-only AI development approaches
More robust and theoretically sound AI algorithms, particularly in reinforcement learning, will be developed.
This improved theoretical understanding will accelerate the deployment of autonomous AI systems with higher reliability and safety assurances.
Increased trust and adoption of AI in critical sectors as the underlying mechanisms become more transparent and provable.
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