Summary of Gaussian Approximation and Multiplier Bootstrap For Polyak-ruppert Averaged Linear Stochastic Approximation with Applications to Td Learning, by Sergey Samsonov et al.
Gaussian Approximation and Multiplier Bootstrap for Polyak-Ruppert Averaged Linear Stochastic Approximation with Applications to TD Learning
by Sergey Samsonov, Eric Moulines, Qi-Man Shao, Zhuo-Song Zhang, Alexey Naumov
First submitted to arxiv on: 26 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR); Statistics Theory (math.ST)
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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 This paper investigates the multivariate normal approximation for Polyak-Ruppert averaged iterates of the linear stochastic approximation (LSA) algorithm, specifically obtaining a Berry-Esseen bound. The authors also establish non-asymptotic confidence intervals for parameter estimation using multiplier bootstrap with LSA. This method updates estimates together with randomly perturbed LSA estimates as new observations arrive. Applications are demonstrated in temporal difference learning with linear function approximation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how to use a special math tool called the Linear Stochastic Approximation (LSA) algorithm to make predictions and estimate things we can’t directly measure. The researchers figured out how to get really good estimates by combining LSA with another technique, called multiplier bootstrap. They tested this method in situations where we want to learn from new data as it arrives. This is useful for tasks like predicting what will happen next based on past patterns. |
