Online Algorithms with Randomly Infused Advice

TL;DR

This paper introduces a new evaluation method called randomly infused advice (RIA) for online algorithms, allowing performance assessment beyond worst-case scenarios by integrating advice from an unreliable oracle.

Contribution

The paper presents RIA, a novel framework that evaluates online algorithms with advice infusion, improving understanding of their performance in more realistic, less adversarial settings.

Findings

Established new upper bounds on competitive ratios for paging, metrical task systems, and set cover with RIA.

Derived tight lower bounds for online algorithms with RIA for the studied problems.

Demonstrated the applicability of RIA to multiple classic online problems.

Abstract

We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any probabilistic assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime. More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer B from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 {\le} {\alpha} {\le} 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - {\alpha}, then the buffer B contains fresh random bits (as in the classic online setting). The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter {\alpha} increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems.