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Warfarin is a widely used anticoagulant, and has a narrow therapeutic range. Dosing of warfarin should be individualized, since slight overdosing or underdosing can have catastrophic or even fatal consequences. Despite much research on warfarin dosing, current dosing protocols do not live up to expectations, especially for patients sensitive to warfarin. We propose a deep reinforcement learning-based dosing model for warfarin. To overcome the issue of relatively small sample sizes in dosing trials, we use a Pharmacokinetic/ Pharmacodynamic (PK/PD) model of warfarin to simulate dose-responses of virtual patients. Applying the proposed algorithm on virtual test patients shows that this model outperforms a set of clinically accepted dosing protocols by a wide margin. We tested the robustness of our dosing protocol on a second PK/PD model and showed that its performance is comparable to the set of baseline protocols.