Reproduce “Optimal Competitive Ratios for Chasing Convex Functions with Quadratic Growth” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Linzhe He, Sifan Yang, Wei Jiang, Lijun Zhang
The authors analyze online convex function chasing, where decisions incur hitting and movement costs. For Euclidean movement, Clipped Proximal Descent combines a proximal step with a clipped correction and achieves ratio 32/7(1+κ^(1/3)) under smoothness and quadratic growth. For squared movement, R-OBD achieves the dimension-uniform optimum 1+q*(λ), without smoothness, matched by a randomized-algorithm lower bound.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.