← 研踪 PaperTrailarXiv:2611.08302 · v1
Dynamic Optimistic Constrained OCO with Memory via Delay Equivalence
首次提交 2026-11-06 01:05
版本更新 2026-11-06 01:05
雷达观测 2026-11-06 12:09
摘要
Online Convex Optimization with memory and time-varying constraints (COCO-M) is a recently-introduced framework that captures the dynamics of stateful online learning and non-stochastic control with budget constraints. Despite its expressive power, COCO-M remains largely understudied. In this work, we tackle this problem in its full scale, providing an optimistic algorithm that incorporates untrusted predictions to tame universal dynamic regret and cumulative constraint violation. Our analysis leverages a potent reduction from memory to delay and treats state-dependent gradients as delayed feedback. We establish the first bounds that adapt to both environment non-stationarity (path length $P_T$) and prediction accuracy, while lifting previous restrictive assumptions such as functional separability. En route to these results, we derive findings of independent interest for the memory-to-delay reduction, and for delayed OCO with time-varying constraints. The proposed framework ensures sublinear worst-case guarantees that improve with prediction accuracy, reaching $\mathcal O(1)$ regret under perfect predictions, with cumulative constraint violation (CCV) $\mathcal O(\sqrt{T})$ for unknown $P_T$ and $\mathcal O(\log T)$ for known or online observable $P_T$ , while recovering the optimal COCO rates when memory disappears.
作者备注：Accepted at the 40th Conference on Neural Information Processing Systems (NeurIPS 2026)
观测到的版本
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v1 · 2026-11-06 01:05 · 最新观测版本
Dynamic Optimistic Constrained OCO with Memory via Delay Equivalence
Online Convex Optimization with memory and time-varying constraints (COCO-M) is a recently-introduced framework that captures the dynamics of stateful online learning and non-stochastic control with budget constraints. Despite its expressive power, COCO-M remains largely understudied. In this work, we tackle this problem in its full scale, providing an optimistic algorithm that incorporates untrusted predictions to tame universal dynamic regret and cumulative constraint violation. Our analysis leverages a potent reduction from memory to delay and treats state-dependent gradients as delayed feedback. We establish the first bounds that adapt to both environment non-stationarity (path length $P_T$) and prediction accuracy, while lifting previous restrictive assumptions such as functional separability. En route to these results, we derive findings of independent interest for the memory-to-delay reduction, and for delayed OCO with time-varying constraints. The proposed framework ensures sublinear worst-case guarantees that improve with prediction accuracy, reaching $\mathcal O(1)$ regret under perfect predictions, with cumulative constraint violation (CCV) $\mathcal O(\sqrt{T})$ for unknown $P_T$ and $\mathcal O(\log T)$ for known or online observable $P_T$ , while recovering the optimal COCO rates when memory disappears.
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