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：我们提出一种新颖方法，用于对在线算法进行严格的定量评估，该方法弱化了经典竞争分析中“极端最坏情况”视角。与先前工作不同，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，也不依赖于特定在线算法的设计。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一种手段。具体而言，采用RIA的在线算法ALG将受益于一个全知但非完全可靠的预言机生成的建议片段。该方法的核心在于：通过将建议写入ALG正常读取随机位的缓冲区B，从而以极其简单且非侵入式的方式增强算法。预言机的（不）可靠性由一个参数0 ≤ α ≤ 1刻画，该参数决定每轮建议被预言机成功注入的概率；若建议未被注入（以概率1-α发生），则缓冲区B包含全新随机位（与经典在线设置一致）。通过将新RIA方法应用于三个被广泛研究的在线问题：分页、统一度量任务系统及在线集合覆盖，我们验证了其适用性。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，该上界随注入参数α增大而改善。同时，针对这三个问题的RIA在线算法，我们还给出了（通常是紧的）竞争比下界。