Attacks on machine learning models have been extensively studied through stateless optimization. In this paper, we demonstrate how a reinforcement learning (RL) agent can learn a new class of attack algorithms that generate adversarial samples. Unlike traditional adversarial machine learning (AML) methods that craft adversarial samples independently, our RL-based approach retains and exploits past attack experience to improve the effectiveness and efficiency of future attacks. We formulate adversarial sample generation as a Markov Decision Process and evaluate RL's ability to (a) learn effective and efficient attack strategies and (b) compete with state-of-the-art AML. On two image classification benchmarks, our agent increases attack success rate by up to 13.2% and decreases the average number of victim model queries per attack by up to 16.9% from the start to the end of training. In a head-to-head comparison with state-of-the-art image attacks, our approach enables an adversary to generate adversarial samples with 17% more success on unseen inputs post-training. From a security perspective, this work demonstrates a powerful new attack vector that uses RL to train agents that attack ML models efficiently and at scale.