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An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo sampling is inefficient. Adaptive importance sampling approaches have been developed for rare event estimation but do not scale well to sequential systems with long horizons. In this work, we develop two adaptive importance sampling algorithms that can efficiently estimate the probability of rare events for sequential decision making systems. The basis for these algorithms is the minimization of the Kullback-Leibler divergence between a state-dependent proposal distribution and a target distribution over trajectories, but the resulting algorithms resemble policy gradient and value-based reinforcement learning. We apply multiple importance sampling to reduce the variance of our estimate and to address the issue of multi-modality in the optimal proposal distribution. We demonstrate our approach on a control task with both continuous and discrete actions spaces and show accuracy improvements over several baselines.