Summary of Prelimit Coupling and Steady-state Convergence Of Constant-stepsize Nonsmooth Contractive Sa, by Yixuan Zhang et al.
Prelimit Coupling and Steady-State Convergence of Constant-stepsize Nonsmooth Contractive SA
by Yixuan Zhang, Dongyan Huo, Yudong Chen, Qiaomin Xie
First submitted to arxiv on: 9 Apr 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR)
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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 The paper studies nonsmooth contractive stochastic approximation (SA) with constant stepsize, motivated by Q-learning. It focuses on two dynamics: nonsmooth contractive SA with additive noise and synchronous and asynchronous Q-learning featuring both additive and multiplicative noise. The paper establishes weak convergence of the iterates to a stationary limit distribution in Wasserstein distance for both dynamics. Additionally, it proposes a prelimit coupling technique for steady-state convergence and characterizes the limit of the stationary distribution as the stepsize goes to zero. The result is used to derive that the asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize, contrasting with smooth SA. This characterization enables the use of Richardson-Romberg extrapolation for bias reduction in nonsmooth SA. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at a way to make computers learn more effectively by studying something called stochastic approximation (SA). It’s based on an idea called Q-learning and involves adding noise to the learning process. The researchers find that as long as the computer learns slowly enough, it will eventually get close to the correct answer, even with noisy data. They also show that the errors in this process go down really quickly when you make the computer learn slower. This is important because it means we can use special tricks to fix these errors and make the computer learn even better. |
