In Imitation Learning, a supervisor’s policy is observed and the intended behavior is learned. A known problem with this approach is covariate shift, which occurs because the agent visits different states than the supervisor. Rolling out the current agent’s policy, an on-policy method, allows for collecting data along a distribution similar to the updated agent’s policy. However this approach can become less effective as the demonstrations are collected in very large batch sizes, which reduces the relevance of data collected in previous iterations. In this paper, we propose to alleviate the covariate shift via the injection of artificial noise into the supervisor’s policy. We prove an improved bound on the loss due to the covariate shift, and introduce an algorithm that leverages our analysis to estimate the level of $\epsilon$-greedy noise to inject. In a driving simulator domain where an agent learns an image-to-action deep network policy, our algorithm Dart achieves a better performance than DAgger with 75% fewer demonstrations.