A Simple Learning-Augmented Algorithm for Online Packing with Concave Objectives
Elena Grigorescu, Young-San Lin, Maoyuan Song
TL;DR
This work addresses online packing problems with a concave objective and uncertain future inputs by introducing a simple switching framework that combines a black-box online algorithm with learning-augmented advice. The main contribution is a general algorithm that, given an $\alpha$-competitive $\beta$-feasible subroutine and advice $x'$, achieves ($2$, $\beta$)-consistency, $2\alpha$-robustness, and $3\beta/2$-feasibility for the packing problem, without requiring access to the internals of the subroutine. The framework is applied to multiple problems—online packing LP, knapsack, resource management, throughput maximization, network utility maximization, and inventory-constrained optimization—with explicit guarantees, and validated by empirical evaluations showing robustness to prediction errors and practical viability. The results highlight a unifying, black-box approach to learning-augmented online algorithms and stimulate further exploration of necessary and sufficient conditions for when simple switching is optimal across broad problem classes.
Abstract
Learning-augmented algorithms has been extensively studied recently in the computer-science community, due to the potential of using machine learning predictions in order to improve the performance of algorithms. Predictions are especially useful for online algorithms making irrevocable decisions without knowledge of the future. Such learning-augmented algorithms aim to overcome the limitations of classical online algorithms when the predictions are accurate, and still perform comparably when the predictions are inaccurate. A common approach is to adapt existing online algorithms to the particular advice notion employed, which often involves understanding previous sophisticated algorithms and their analyses. However, ideally, one would simply use previous online solutions in a black-box fashion, without much loss in the approximation guarantees. Such clean solutions that avoid opening up black-boxes are often rare, and may be even missed the first time around. For example, Grigorescu et al. (NeurIPS 22) proposed a learning-augmented algorithms for online covering linear programs, but it later turned out that their results can be subsumed by a natural approach that switches between the advice and an online algorithm given as a black-box, as noted in their paper. In this work, we introduce and analyze a simple learning-augmented algorithm for online packing problems with linear constraints and concave objectives. We exhibit several direct applications of our framework including online packing linear programming, knapsack, resource management benefit, throughput maximization, and network utility maximization. We further raise the problem of understanding necessary and sufficient conditions for when such simple black-box solutions may be optimal. We believe this is an important direction of research that would unify many ad-hoc approaches from the literature.