Convergence Rate in Nonlinear Two-Time-Scale Stochastic Approximation with State (Time)-Dependence
Not on the map. Why?
Abstract (arXiv)
The nonlinear two-time-scale stochastic approximation is widely studied under conditions of bounded variances in noise. Motivated by recent advances that allow for variability linked to the current state or time, we consider state- and time-dependent noises. We show that the Lyapunov function exhibits polynomial convergence rates in both cases, with the rate of polynomial delay depending on the parameters of state- or time-dependent noises. Notably, if the state noise parameters fully approach their limiting value, the Lyapunov function achieves an exponential convergence rate. We provide two numerical examples to illustrate our theoretical findings in the context of stochastic gradient descent with Polyak-Ruppert averaging and stochastic bilevel optimization.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 9 of its 26 references that are in the map. First posted on arXiv 14 Sep 2025.
Builds on
9 of 26 references.
References · 9
- 2016Optimization Methods for Large-Scale Machine Learningcited by 1,150
- 2020A Finite Time Analysis of Two Time-Scale Actor Critic Methodscited by 122
- 2016Statistical Inference for Model Parameters in Stochastic Gradient Descentcited by 71
- 2020Finite Time Analysis of Linear Two-timescale Stochastic Approximation with Markovian Noisecited by 53
- 2020Nonlinear Two-Time-Scale Stochastic Approximation: Convergence and Finite-Time Performancecited by 35
- 2019Two Time-scale Off-Policy TD Learning: Non-asymptotic Analysis over Markovian Samplescited by 31
- 2022A Single-Timescale Analysis For Stochastic Approximation With Multiple Coupled Sequencescited by 17
- 2023Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applicationscited by 15
- 2024Finite-Time Decoupled Convergence in Nonlinear Two-Time-Scale Stochastic Approximationcited by 10
Built on by
Not cited yet.