Finite-Time Analysis of Projected Two-Time-Scale Stochastic Approximation

ArXi:2604.00179v1 Announce Type: cross 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.