Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of
dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods.
Yet it remains unclear to what extent such acceleration can be achieved for general $\ell_p$ smooth functions.
In this paper, we propose a new accelerated first-order method for convex optimization under non-Euclidean smoothness assumptions.
In contrast to standard acceleration techniques, our approach uses primal-dual iterate sequences taken with respect to differing norms,
which are then coupled using an implicitly determined interpolation parameter. For