This paper introduces a new model for ML-augmented online decision making, called online algorithms with unreliable guidance (OAG). This model completely separates between the predictive and algorithmic components, thus offering a single well-defined analysis framework that relies solely on the considered problem. Formulated through the lens of request-answer games, an OAG algorithm receives, with each incoming request, a piece of guidance which is taken from the problem's answer space; ideally, this guidance is the optimal answer for the current request, however with probability $β$, the guidance is adversarially corrupted. The goal is to develop OAG algorithms that admit good competitiveness when $β= 0$ (a.k.a. consistency) as well as when $β= 1$ (a.k.a. robustness); the appealing notion of smoothness, that in most prior work required a dedicated loss function, now arises naturally as $β$ shifts from $0$ to $1$. We then describe a systematic method, called the drop or trust blindly (DTB) compiler, which transforms any online algorithm into a learning-augmented online algorithm in the OAG model. Given a prediction-oblivious online algorithm, its learning-augmented counterpart produced by applying the DTB compiler either follows the incoming guidance blindly or ignores it altogether and proceeds as the initial algorithm would have; the choice between these two alternatives is based on the outcome of a (biased) coin toss. As our main technical contribution, we prove (rigorously) that although remarkably simple, the class of algorithms produced via the DTB compiler includes algorithms with attractive consistency-robustness guarantees for three classic online problems: for caching and uniform metrical task systems our algorithms are optimal, whereas for bipartite matching (with adversarial arrival order), our algorithm outperforms the state-of-the-art.

翻译：本文提出了一种新的机器学习增强在线决策模型，称为不可靠指导下的在线算法（OAG）。该模型完全分离了预测组件与算法组件，从而提供了一个仅依赖于所考虑问题的、定义明确的分析框架。通过请求-应答博弈的视角进行形式化，OAG算法在接收到每个传入请求时，会获得一条取自问题应答空间的指导信息；理想情况下，该指导是当前请求的最优应答，然而以概率 $β$ 计，该指导可能遭受对抗性篡改。我们的目标是开发这样的OAG算法：当 $β= 0$（即一致性）以及当 $β= 1$（即鲁棒性）时均能保持良好的竞争比；平滑性这一吸引人的概念——在以往大多数工作中需要专门定义损失函数——现在随着 $β$ 从 $0$ 变化到 $1$ 而自然涌现。随后，我们描述了一种系统化方法，称为“丢弃或盲目信任”（DTB）编译器，它能够将任何在线算法转化为OAG模型下的学习增强型在线算法。给定一个不考虑预测的在线算法，通过应用DTB编译器产生的学习增强版本要么盲目跟随传入的指导，要么完全忽略指导并按初始算法的方式执行；这两种选择之间的决策基于一次（有偏的）硬币抛掷结果。作为我们的主要技术贡献，我们（严格地）证明：尽管极其简单，但通过DTB编译器产生的算法类别包含了针对三个经典在线问题具有吸引人的一致性-鲁棒性保证的算法：对于缓存和均匀度量任务系统，我们的算法是最优的；而对于二分图匹配（在对抗性到达顺序下），我们的算法超越了现有最佳方法。