Online Selection Problems against Constrained Adversary

Inspired by a recent line of work in online algorithms with predictions, we study the constrained adversary model that utilizes predictions from a different perspective. Prior works mostly focused on designing simultaneously robust and consistent algorithms, without making assumptions on the quality of the predictions. In contrary, our model assumes the adversarial instance is consistent with the predictions and aim to design algorithms that have best worst-case performance against all such instances. We revisit classical online selection problems under the constrained adversary model. For the single item selection problem, we design an optimal algorithm in the adversarial arrival model and an improved algorithm in the random arrival model (a.k.a., the secretary problem). For the online edge-weighted bipartite matching problem, we extend the classical Water-filling and Ranking algorithms and achieve improved competitive ratios.