  In smooth strongly convex optimization, knowledge of the strong convexity
parameter is critical for obtaining simple methods with accelerated rates. In
this work, we study a class of methods, based on Polyak steps, where this
knowledge is substituted by that of the optimal value, $f_*$. We first show
slightly improved convergence bounds than previously known for the classical
case of simple gradient descent with Polyak steps, we then derive an
accelerated gradient method with Polyak steps and momentum, along with
convergence guarantees.
