Online Algorithms with Unreliable Guidance

Abstract: 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.