Approximations and Learning for Continuous State and Action MDPs under Average Cost Criteria

2025-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A 2026 paper by Ali D. Kara and Serdar Yüksel, published in JMLR 27(68):1−50, introduces methods for Markov Decision Processes (MDPs) with continuous state and action spaces under average cost criteria. The research first details a discretization-based approximation technique for these continuous MDPs, providing error bounds for approximations. This method relaxes previous total variation conditions to weak continuity or Wasserstein continuity, assuming certain ergodicity. Second, the authors present synchronous and asynchronous Q-learning algorithms designed for continuous spaces, utilizing quantization where the quantized state acts as the actual state in the algorithms. The paper establishes the convergence of these Q-learning algorithms. Finally, it demonstrates that this convergence leads to the optimal Q values of a finite approximate model built through quantization, indicating the near-optimality of the resulting solution.

Key takeaway

For Reinforcement Learning Engineers designing algorithms for continuous control problems, this research offers a robust pathway. You can now confidently apply Q-learning to continuous state and action MDPs by leveraging quantization, knowing it converges to near-optimal solutions. This relaxes prior strict continuity assumptions, broadening the applicability of average cost criteria. Consider integrating these discretization and quantization techniques into your continuous reinforcement learning frameworks.

Key insights

Discretization and quantized Q-learning enable near-optimal solutions for continuous MDPs under average cost.

Principles

• Weak or Wasserstein continuity can replace total variation for error bounds.
• Quantization facilitates Q-learning in continuous state spaces.
• Convergence to finite approximate model implies near-optimality.

Method

The approach involves discretizing continuous MDPs, then applying synchronous or asynchronous Q-learning with quantized states, ensuring convergence to near-optimal Q values.

In practice

• Apply quantization to adapt Q-learning for continuous environments.
• Use weak or Wasserstein continuity for error analysis in continuous MDPs.

Topics

• Markov Decision Processes
• Continuous Control
• Q-learning
• Quantization
• Average Cost Criteria
• Error Bounds

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.