Online Ranking Learning (OLTR) plays a crucial role in information retrieval and machine learning systems and is widely applied to search engines and content recommenders. However, despite its widespread use, there is a lack of understanding of the vulnerability of the OLTR algorithm to systematic adversarial attacks. In this study, we present a novel framework for attacking the widely used OLTR algorithm. This framework is designed to induce linear regret in the learning algorithm while ensuring that the target item set appears in the top K recommendation lists within T - o(T) rounds. We propose two novel attack strategies: CascadeOFA for CascadeUCB1 and PBMOFA for PBM-UCB. Both strategies provide theoretical guarantees that only O(log T) operations are required for success. We further complement our theoretical analysis with experimental results on real-world data.