Title: Efficient Competitive Self-Play Policy Optimization. Abstract: Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are designed to choose an opponent for the current learner. Typical rules include choosing the latest agent, the best agent, or a random historical agent. However, these rules may be inefficient in practice and sometimes do not guarantee convergence even in the simplest matrix games. This paper proposes a new algorithmic framework for competitive self-play reinforcement learning in two-player zero-sum games. We recognize the fact that the Nash equilibrium coincides with the saddle point of the stochastic payoff function, which motivates us to borrow ideas from classical saddle point optimization literature. Our method simultaneously trains several agents and intelligently takes each other as opponents based on a simple adversarial rule derived from a principled perturbation-based saddle optimization method. We prove theoretically that our algorithm converges to an approximate equilibrium with high probability in convex-concave games under standard assumptions. Beyond the theory, we further show the empirical superiority of our method over baseline methods relying on the aforementioned opponent-selection heuristics in matrix games, grid-world soccer, Gomoku, and simulated robot sumo, with neural net policy function approximators.