Dimension-Optimal Dynamic Regret in Exp-Concave Online Learning

Key points

• Tracking changing comparators is a central problem in online learning.1
• For exp-concave losses, previous work established the $T^{1/3}PT^{2/3}$ dependence on the horizon $T$ and Euclidean path length $PT$ for fixed dimension, while the optimal cost of dimension remained unresolved.1
• We resolve this question by establishing a sharp $d^{1/3}$ curved dimension factor, improving the $d^{2/3}$ factor of recent switching and interval reductions [1, 2].1
• The curved learner maintains $O(\log^2 T)$ Gaussian states, uses one gradient per round, and runs in time near-linear in $T$ under a Mahalanobis-projection oracle.1

Sources (1)

• [1]Dimension-Optimal Dynamic Regret in Exp-Concave Online Learning
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 01:37 PM

  To achieve this improvement, we develop a proper, full-information learner on compact convex subsets of $\mathbb{R}^d$ that adapts to the unknown path length and, under fixed dimension-independent diameter, gradient, and curvature parameters, guarantees

  Tracking changing comparators is a central problem in online learning.

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