English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Stochastic approximation (SA) with multiple coupled sequences has found broadapplications in machine learning such as bilevel learning and reinforcementlearning (RL). In this paper, we study the finite-time convergence of nonlinearSA with multiple coupled sequences. Different from existing multi-timescaleanalysis, we seek for scenarios where a fine-grained analysis can provide thetight performance guarantee for multi-sequence single-timescale SA (STSA). Atthe heart of our analysis is the smoothness property of the fixed points inmulti-sequence SA that holds in many applications. When all sequences havestrongly monotone increments, we establish the iteration complexity of$\mathcal{O}(\epsilon^{-1})$ to achieve $\epsilon$-accuracy, which improves theexisting $\mathcal{O}(\epsilon^{-1.5})$ complexity for two coupled sequences.When all but the main sequence have strongly monotone increments, we establishthe iteration complexity of $\mathcal{O}(\epsilon^{-2})$. The merit of ourresults lies in that applying them to stochastic bilevel and compositionaloptimization problems, as well as RL problems leads to either relaxedassumptions or improvements over their existing performance guarantees.

A Single-Timescale Analysis For Stochastic Approximation With Multiple Coupled Sequences