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：我们提出了一种新颖的方法，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”的视角。与先前工作不同，我们的方法（称为随机注入建议，RIA）不对输入序列做任何概率假设，也不依赖于特定在线算法的开发。相反，它可以应用于现有的在线随机算法，为评估其在非极端最坏情况场景下的性能提供了一种手段。具体而言，采用RIA的在线算法ALG受益于由全知但并非完全可靠的预言机生成的建议。该新方法的关键在于，通过将建议写入缓冲区B来提供给ALG，而ALG通常从该缓冲区读取随机比特，从而允许我们通过一个非常简单且非侵入式的接口对其进行增强。预言机的（不）可靠性通过参数0 ≤ α ≤ 1来刻画，该参数决定每个回合中建议被预言机成功注入的概率；若建议未被注入（概率为1 - α），则缓冲区B包含新的随机比特（如同经典在线设置）。通过将RIA新方法应用于三个广泛研究的在线问题——分页、统一度量任务系统和在线集合覆盖——我们展示了其适用性。针对这些问题，我们为经典在线算法建立了新的竞争比上界，这些上界随着注入参数α的增加而改进。同时，我们还为这三个问题中采用RIA的在线算法补充了（通常紧的）竞争比下界。