arXiv:2604.19569v4 Announce Type: replace Abstract: Q-learning is a fundamental algorithmic primitive in reinforcement learning. This paper develops a new framework for analyzing Q-learning from a switching linear system (SLS) viewpoint. In particular, we derive a stochastic SLS representation of the Q-learning error, and a finite-time error analysis through the joint spectral radius (JSR) of the corresponding SLS model, where the JSR is the exact worst-case exponential rate of the associated SLS. To the best of our knowledge, this is the first convergence rate analysis of standard Q-learning
This publication represents a detailed theoretical advancement in an active field of AI research, building on fundamental reinforcement learning algorithms. The timing reflects ongoing efforts to enhance the stability and predictability of AI, coinciding with rising interest in robust agentic systems.
Improved theoretical understanding and convergence analysis of Q-learning can lead to more reliable, efficient, and scalable reinforcement learning agents. This foundational work potentially unlocks more effective deployment of AI in complex, real-world scenarios where stability is critical.
The development of a Lyapunov-certified framework provides a new method for analyzing and potentially improving the stability and finite-time error rates of Q-learning algorithms. This changes how researchers can approach the design and guarantees of certain reinforcement learning systems.
- · AI researchers
- · Reinforcement learning developers
- · Companies deploying autonomous AI systems
More stable and predictable Q-learning algorithms can be developed and integrated into various AI applications.
Enhanced reliability of reinforcement learning could accelerate the development and adoption of AI agents in mission-critical applications.
Increased trustworthiness of autonomous AI systems could reduce regulatory friction and expand the scope of AI applications across industries.
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