arXiv:2509.26442v2 Announce Type: replace Abstract: The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and reinforcement learning (RL). However, its original form has a significant limitation as it requires the zero-order term to be summable. In many important RL applications, this summable condition, however, cannot be met. This limitation motivates us to extend the Robbins-Siegmund theorem for almost supermart
Ongoing research in machine learning constantly seeks to improve the theoretical underpinnings of existing algorithms, especially as real-world applications of AI become more complex and widespread.
Improved theoretical guarantees for stochastic iterative algorithms in reinforcement learning can lead to more robust, reliable, and efficient AI systems, especially in scenarios where traditional assumptions are not met.
The ability to relax the summable condition in the Robbins-Siegmund theorem expands the applicability of these convergence analyses to a wider range of reinforcement learning problems that were previously difficult to formally guarantee.
- · AI researchers
- · Reinforcement learning applications
- · Robotics
- · Autonomous systems
- · Inefficient RL algorithms dependent on restrictive theoretical assumptions
The immediate impact is a stronger theoretical foundation for certain classes of reinforcement learning algorithms.
This improved theory could accelerate the development and deployment of more advanced and provably convergent AI agents in complex environments.
More robust RL could contribute to the societal adoption of AI in critical applications, driving demand for compute and related infrastructure.
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Read at arXiv cs.LG