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The interaction between a vehicle navigation system and the driver of the vehicle can be formulated as a model-based reinforcement learning problem, where the navigation systems (agent) must quickly adapt to the characteristics of the driver (environmental dynamics) to provide the best sequence of turn-by-turn driving instructions. Most modern day navigation systems (e.g, Google maps, Waze, Garmin) are not designed to personalize their low-level interactions for individual users across a wide range of driving styles (e.g., vehicle type, reaction time, level of expertise). Towards the development of personalized navigation systems that adapt to a variety of driving styles, we propose an online no-regret model-based RL method that quickly conforms to the dynamics of the current user. As the user interacts with it, the navigation system quickly builds a user-specific model, from which navigation commands are optimized using model predictive control. By personalizing the policy in this way, our method is able to give well-timed driving instructions that match the user's dynamics. Our theoretical analysis shows that our method is a no-regret algorithm and we provide the convergence rate in the agnostic setting. Our empirical analysis with 60+ hours of real-world user data using a driving simulator shows that our method can reduce the number of collisions by more than 60%.