تقرير
Central Limit Theorem for Two-Timescale Stochastic Approximation with Markovian Noise: Theory and Applications
| العنوان: | Central Limit Theorem for Two-Timescale Stochastic Approximation with Markovian Noise: Theory and Applications |
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| المؤلفون: | Hu, Jie, Doshi, Vishwaraj, Eun, Do Young |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Computer Science - Machine Learning, Mathematics - Optimization and Control |
| الوصف: | Two-timescale stochastic approximation (TTSA) is among the most general frameworks for iterative stochastic algorithms. This includes well-known stochastic optimization methods such as SGD variants and those designed for bilevel or minimax problems, as well as reinforcement learning like the family of gradient-based temporal difference (GTD) algorithms. In this paper, we conduct an in-depth asymptotic analysis of TTSA under controlled Markovian noise via central limit theorem (CLT), uncovering the coupled dynamics of TTSA influenced by the underlying Markov chain, which has not been addressed by previous CLT results of TTSA only with Martingale difference noise. Building upon our CLT, we expand its application horizon of efficient sampling strategies from vanilla SGD to a wider TTSA context in distributed learning, thus broadening the scope of Hu et al. (2022). In addition, we leverage our CLT result to deduce the statistical properties of GTD algorithms with nonlinear function approximation using Markovian samples and show their identical asymptotic performance, a perspective not evident from current finite-time bounds. Comment: To appear in AISTATS 2024 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.09339 |
| رقم الأكسشن: | edsarx.2401.09339 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |