Universal Online Convex Optimization With Delayed Feedback

Key points

• We develop a single algorithm that simultaneously adapts to general convex, strongly convex, and exp-concave losses without prior knowledge of the curvature class or parameters.1
• Our regret bounds match the best known dependence on the time horizon $T$ and delays up to doubly logarithmic factors: roughly $\sqrt{T + d{tot}}$ for convex losses and $σ{\max}\log T$ rates with curved losses, where $d{tot}$ is the total cumulative delay and $σ{\max}$ is the maximum number of simultaneously missing observations.1
• Our main technical contribution is a delayed meta-learner with a second-order excess-loss guarantee, which enables curvature-adaptive aggregation of delayed base learners.1
• In addition, our new exp-concave base learner yields a sharper regret bound which improves the state-of-the-art delay dependence by replacing the maximum delay with the potentially much smaller $σ{\max}$, while retaining the complementary $\sqrt{d{tot}}$ dependence.1

Sources (1)

• [1]Universal Online Convex Optimization With Delayed Feedback
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 11:46 AM

  We study universal online convex optimization with delayed feedback.

  We develop a single algorithm that simultaneously adapts to general convex, strongly convex, and exp-concave losses without prior knowledge of the curvature class or parameters.

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