Faster Acceleration for Steepest Descent
<|reference_start|>Faster Acceleration for Steepest Descent: 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 $\ell_p$ norm smooth problems in $d$ dimensions, our method provides an iteration complexity improvement of up to $O(d^{1-\frac{2}{p}})$ in terms of calls to a first-order oracle, thereby allowing us to circumvent long-standing barriers in accelerated non-Euclidean steepest descent.<|reference_end|>
@article{bai2024faster,
    title={Faster Acceleration for Steepest Descent},
    author={Site Bai and Brian Bullins},
    journal={arXiv preprint arXiv:2409.19200},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.19200},
    primaryClass={math.OC cs.LG stat.ML}
}