Finite-Time Analysis of Projected Two-Time-Scale Stochastic Approximation
We study the finite-time convergence of projected linear two-time-scale stochastic approximation with constant step sizes and Polyak--Ruppert averaging. We establish an explicit mean-square error bound, decomposing it into two interpretable components, an approximation error determined by the constrained subspace and a statistical error decaying at a sublinear rate, with constants expressed through restricted stability margins and a coupling invertibility condition. These constants cleanly separate the effect of subspace choice (approximation errors) from the effect of the averaging horizon (statistical errors). We illustrate our theoretical results through a number of numerical experimen...
| Authors | Yitao Bai, Thinh T. Doan, Justin Romberg |
|---|---|
| Primary category | eess.SY |
| Published | 31 March 2026 |
| Last updated at source | 31 March 2026 |
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