Learning-Augmented and Randomized Algorithms for Line Aggregation with Delays

2026-07-30

AI Summary

This work addresses the online linear aggregation problem with delay, aiming to balance algorithmic performance both with and without access to predictions. It proposes the first learning-augmented online algorithms—both deterministic and randomized—with rigorous theoretical guarantees. The deterministic algorithm achieves a robustness bound of $(4/\lambda + 1/\lambda^2)$ and a consistency bound of $(4+\lambda)$. The randomized algorithm attains a competitive ratio of $(e+1)$ against an oblivious adversary, surpassing the known lower bound for deterministic algorithms and improving the previous lower bound for randomized algorithms to $e$. The efficacy of the proposed methods is substantiated through comprehensive theoretical analysis and numerical experiments.

Abstract

This paper studies learning-augmented and randomized online aggregation with delays on a line metric. We consider advice given as online suggested service lengths, and evaluate the algorithms in terms of robustness and consistency. For each $λ\in (0,1]$, we first propose a deterministic learning-augmented \textsc{Balance} algorithm that is $(4/λ+1/λ^2)$-robust and $(4+λ)$-consistent. We also propose a randomized algorithm for the problem in the classical adversarial model, which is $(e+1)$-competitive against an oblivious adversary, improving over the deterministic $5$-competitive \textsc{Balance} benchmark~\cite{bienkowski2013chain}. Notably, this competitive ratio is even lower than the lower bound of $4$ for deterministic online algorithms. Moreover, we establish a lower bound of $e$ on the competitive ratio of randomized online algorithms, improving the previous lower bound of $e/(e-1)$. Besides, we combine the two ideas and obtain a randomized learning-augmented algorithm that is $(e/λ+1/λ^2)$-robust and $(e+λ)$-consistent. Finally, we conduct numerical experiments to complement our theoretical analysis and evaluate the empirical performance of our algorithms.

Problem

• online aggregation
• delays
• learning-augmented algorithms
• randomized algorithms
• line metric

Innovation

• learning-augmented algorithms
• randomized algorithms
• online aggregation with delays
• competitive analysis
• robustness and consistency