arXiv:2606.16846v1 Announce Type: cross Abstract: We study the operator-theoretic core of Q-learning in continuous-time stochastic control with continuous states and actions. In value-based reinforcement learning, each Q-learning or DQN update is built from a Bellman optimality target; our analysis isolates this target in a diffusion setting and studies its regularity and approximation complexity. Under uniform ellipticity and H\"older-regular coefficients, we show that a Bellman update maps bounded inputs into an anisotropic regularity class, smoothing the state variable while leaving only Li
The paper provides a theoretical advancement in understanding continuous-time Q-learning, crucial for developing more robust and sophisticated AI agents in complex environments.
This research offers fundamental insights into the mathematical properties of advanced AI learning algorithms, which is essential for pushing the boundaries of autonomous systems.
Our understanding of the theoretical underpinnings of Q-learning in continuous stochastic environments is enhanced, which will inform future algorithmic design and deployment.
- · AI researchers
- · Robotics companies
- · Autonomous systems developers
- · AI companies reliant on heuristic approaches without strong theoretical foundati
Improved theoretical understanding accelerates the development of more stable and effective reinforcement learning algorithms for continuous control tasks.
Advanced Q-learning techniques enable AI agents to handle real-world complexities, leading to breakthroughs in areas like autonomous driving or industrial automation.
More capable and reliable AI agents contribute to broader adoption of AI across critical sectors, potentially leading to increased demand for specialized hardware and infrastructure.
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Read at arXiv cs.AI