  In the context of statistical supervised learning, the noiseless linear model
assumes that there exists a deterministic linear relation $Y = \langle
\theta_*, X \rangle$ between the random output $Y$ and the random feature
vector $\Phi(U)$, a potentially non-linear transformation of the inputs $U$. We
analyze the convergence of single-pass, fixed step-size stochastic gradient
descent on the least-square risk under this model. The convergence of the
iterates to the optimum $\theta_*$ and the decay of the generalization error
follow polynomial convergence rates with exponents that both depend on the
regularities of the optimum $\theta_*$ and of the feature vectors $\Phi(u)$. We
interpret our result in the reproducing kernel Hilbert space framework. As a
special case, we analyze an online algorithm for estimating a real function on
the unit interval from the noiseless observation of its value at randomly
sampled points; the convergence depends on the Sobolev smoothness of the
function and of a chosen kernel. Finally, we apply our analysis beyond the
supervised learning setting to obtain convergence rates for the averaging
process (a.k.a. gossip algorithm) on a graph depending on its spectral
dimension.
