Revisiting Smoothed Online Learning: Competitive Ratio, Dynamic Regret with Switching Cost, and Best of Both Worlds

We revisit smoothed online learning and develop algorithms with improved competitive ratios, optimal dynamic regret with switching cost, and best-of-both-worlds guarantees. Surprisingly, minimizing the hitting cost alone is $\max(1,\frac{2}α)$-competitive for $α$-polyhedral functions under the $\ell