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.

翻译：我们提出一种新方法，用于对在线算法进行严格的定量评估，该方法放宽了经典竞争分析中“极端最坏情况”视角的限制。与先前研究不同，我们的方法称为随机注入建议（RIA），既不对输入序列做任何概率假设，也不依赖开发专门的在线算法。相反，它可以应用于现有的在线随机算法，为评估这些算法在超出极端最坏情况场景下的性能提供了一种途径。具体而言，采用RIA的在线算法ALG从全知但并非完全可靠的神谕生成的建议中获益。该方法的关键在于，通过将建议写入ALG通常用于读取随机比特的缓冲区B，从而实现以极简单且非侵入式的接口增强算法。神谕的（不）可靠性通过参数0≤α≤1来刻画，该参数决定每轮建议被成功注入的概率；若建议未被注入（概率为1-α），则缓冲区B包含全新随机比特（与经典在线场景一致）。通过将RIA方法应用于三个广泛研究的在线问题：分页、均匀度量任务系统和在线集合覆盖，我们验证了其适用性。针对这些问题，我们建立了经典在线算法竞争比的新上界，该上界随注入参数α增大而改善。同时，我们还为这三个问题提供了在线算法（通常紧的）下界。