aiqbench analysis
This research advances online convex optimization by introducing a meta-learning framework that effectively handles fixed penalties for changing model deployments, addressing a critical gap in tracking dynamic comparators. The proposed algorithm achieves minimax-optimal regret bounds without requiring prior knowledge of switch frequencies or path lengths, offering robust theoretical guarantees for real-world systems with startup overheads.
Dynamic Regret in Online Convex Optimization with Indicator Switching Costs
arXiv:2609.30556v1 Announce Type: new Abstract: We study dynamic regret in online convex optimization with an \emph{indicator switching cost}: a fixed penalty incurred whenever two consecutive decisions differ. This captures startup overheads such as server activation, model deployment, and cache updates, and on a bounded domain it recovers norm-based movement costs as a special case. Existing guarantees for indicator costs handle only static comparators. We show that a direct extension of these techniques to dynamic regret provably fails, motivating a different approach. We propose a meta-learning framework: a set of randomized lazy FTRL base learners restarted at dyadic time scales, aggregated by a movement-aware master that mixes their proposal densities and samples actions via maximal coupling of consecutive mixtures. The resulting algorithm satisfies, in expectation, $\mathcal{R}^{\mathbf{1}}_T \le \tilde{\mathcal{O}}(\min\{\sqrt{T(S_T{+}1)},T^{2/3}(P_T+1)^{1/3}\})$, where $\mathcal{R}^{\mathbf{1}}_T$ is the dynamic regret plus the cumulative indicator switching cost, $S_T$ counts comparator switches, and $P_T$ is the comparator path length. The bound holds simultaneously for all sequences and requires no prior knowledge of $S_T$ or $P_T$: it is minimax-optimal (up to logarithmic factors) for tracking piecewise-constant comparators, and also captures frequently moving comparators with small total path length.
Abstract:We study dynamic regret in online convex optimization with an \emph{indicator switching cost}: a fixed penalty incurred whenever two consecutive decisions differ. This captures startup overheads such as server activation, model deployment, and cache updates, and on a bounded domain it recovers norm-based movement costs as a special case. Existing guarantees for indicator costs handle only static comparators. We show that a direct extension of these techniques to dynamic regret provably fails, motivating a different approach. We propose a meta-learning framework: a set of randomized lazy FTRL base learners restarted at dyadic time scales, aggregated by a movement-aware master that mixes their proposal densities and samples actions via maximal coupling of consecutive mixtures. The resulting algorithm satisfies, in expectation, $\mathcal{R}^{\mathbf{1}}_T \le \tilde{\mathcal{O}}(\min\{\sqrt{T(S_T{+}1)},T^{2/3}(P_T+1)^{1/3}\})$, where $\mathcal{R}^{\mathbf{1}}_T$ is the dynamic regret plus the cumulative indicator switching cost, $S_T$ counts comparator switches, and $P_T$ is the comparator path length. The bound holds simultaneously for all sequences and requires no prior knowledge of $S_T$ or $P_T$: it is minimax-optimal (up to logarithmic factors) for tracking piecewise-constant comparators, and also captures frequently moving comparators with small total path length.
Machine Learning (cs.LG)
arXiv:2609.30556 [cs.LG]
(or arXiv:2609.30556v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.30556 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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