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New research details phase transition in stochastic approximation, offers solution

By PulseAugur Editorial · [2 sources] ·

Researchers have identified a sharp phase transition in nonlinear two-time-scale stochastic approximation, impacting the convergence rates of slow iterates. The study reveals that without modifications, the recursion's mean-square rate is generally $k^{-a}$, with a decoupled $k^{-1}$ rate only achievable under strong local linearity. By introducing an auxiliary online bias estimator, the researchers demonstrate that a $O(k^{-1})$ rate can be achieved across all regimes, overcoming the previously identified limitations. AI

RANK_REASON The cluster contains a research paper published on arXiv detailing theoretical advancements in stochastic approximation.

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AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New research details phase transition in stochastic approximation, offers solution

COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Dhruv Sarkar, Vaneet Aggarwal ·

    Nonlinear Two-Time-Scale Stochastic Approximation: A Sharp Phase Transition and How to Beat It

    arXiv:2606.14488v1 Announce Type: cross Abstract: Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, …

  2. arXiv cs.LG TIER_1 English(EN) · Vaneet Aggarwal ·

    Nonlinear Two-Time-Scale Stochastic Approximation: A Sharp Phase Transition and How to Beat It

    Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $β_k=Θ(k^{-1})$ and $α_k=Θ(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $…

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