Summary of Asymptotic and Finite Sample Analysis Of Nonexpansive Stochastic Approximations with Markovian Noise, by Ethan Blaser et al.
Asymptotic and Finite Sample Analysis of Nonexpansive Stochastic Approximations with Markovian Noise
by Ethan Blaser, Shangtong Zhang
First submitted to arxiv on: 29 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Optimization and Control (math.OC); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Medium Difficulty Summary: This paper focuses on stochastic approximation algorithms driven by nonexpansive operators, unlike previous research on contractive operators. The authors investigate nonexpansive stochastic approximations with Markovian noise, providing both asymptotic and finite-sample analysis. Key to their analysis are novel bounds of noise terms derived from the Poisson equation. As an application, they prove that tabular average reward temporal difference learning converges to a sample-path-dependent fixed point for the first time. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Low Difficulty Summary: This paper is about improving how machines learn by creating new types of algorithms. Instead of using old methods, the researchers try something new: they use operators that are not too “expansive” or contractive. They study this new approach and find it works well with noise from a certain type of process called Markovian noise. The results show that a classic learning method actually converges to a specific point when used with this new algorithm. |
