Robust Online Learning for Resource Allocation -- Beyond Euclidean Projection and Dynamic Fit

TL;DR

This paper introduces a new performance measure for online resource allocation algorithms and proposes non-causal methods that achieve sub-linear growth of constraint violations in changing environments, outperforming existing approaches.

Contribution

The paper presents a novel performance measure, $ ext{ extbackslash hCFit}$, and develops non-causal algorithms that improve constraint violation management in online learning beyond Euclidean projections.

Findings

Sub-linear growth of $ ext{ extbackslash hCFit}$ in slowly changing environments.

Numerical experiments show performance gains over state-of-the-art methods.

Algorithms effectively handle noisy first-order feedback.

Abstract

Online-learning literature has focused on designing algorithms that ensure sub-linear growth of the cumulative long-term constraint violations. The drawback of this guarantee is that strictly feasible actions may cancel out constraint violations on other time slots. For this reason, we introduce a new performance measure called $\hCFit$, whose particular instance is the cumulative positive part of the constraint violations. We propose a class of non-causal algorithms for online-decision making, which guarantees, in slowly changing environments, sub-linear growth of this quantity despite noisy first-order feedback. Furthermore, we demonstrate by numerical experiments the performance gain of our method relative to the state of art.