The implications of the weaker assumptions in this work compared to prior results have significant implications for the practical applicability in reinforcement learning. By relaxing certain assumptions, such as the requirement for specific types of noise or the boundedness of certain functions, the analysis becomes more versatile and applicable to a wider range of scenarios.
In practical reinforcement learning settings, where the noise may not always conform to strict assumptions, the ability to work with more general conditions allows for a more realistic and robust analysis of algorithms. The weaker assumptions enable the results to be more widely applicable across different reinforcement learning algorithms and scenarios, providing a more flexible framework for understanding the stability and convergence properties of these algorithms.
Additionally, the practical applicability of the results is enhanced by the ability to handle a broader range of noise types and conditions, making the analysis more relevant to real-world applications. By relaxing certain assumptions while still maintaining rigorous analysis techniques, the work becomes more accessible and useful for researchers and practitioners in the field of reinforcement learning.