A deep reinforcement learning (DRL) agent observes its states through\nobservations, which may contain natural measurement errors or adversarial\nnoises. Since the observations deviate from the true states, they can mislead\nthe agent into making suboptimal actions. Several works have shown this\nvulnerability via adversarial attacks, but existing approaches on improving the\nrobustness of DRL under this setting have limited success and lack for\ntheoretical principles. We show that naively applying existing techniques on\nimproving robustness for classification tasks, like adversarial training, is\nineffective for many RL tasks. We propose the state-adversarial Markov decision\nprocess (SA-MDP) to study the fundamental properties of this problem, and\ndevelop a theoretically principled policy regularization which can be applied\nto a large family of DRL algorithms, including proximal policy optimization\n(PPO), deep deterministic policy gradient (DDPG) and deep Q networks (DQN), for\nboth discrete and continuous action control problems. We significantly improve\nthe robustness of PPO, DDPG and DQN agents under a suite of strong white box\nadversarial attacks, including new attacks of our own. Additionally, we find\nthat a robust policy noticeably improves DRL performance even without an\nadversary in a number of environments. Our code is available at\nhttps://github.com/chenhongge/StateAdvDRL.\n