Title: Policy Learning Using Weak Supervision. Abstract: Most existing policy learning solutions require the learning agents to receive high-quality supervision signals, e.g., rewards in reinforcement learning (RL) or high-quality expert demonstrations in behavior cloning (BC). These quality supervisions are either infeasible or prohibitively expensive to obtain in practice. We aim for a unified framework that leverages the weak supervisions to perform policy learning efficiently. To handle this problem, we treat the ``weak supervisions'' as imperfect information coming from a \emph{peer agent}, and evaluate the learning agent's policy based on a  ``correlated agreement'' with the peer agent's policy (instead of simple agreements). Our way of leveraging peer agent's information offers us a family of solutions that learn effectively from weak supervisions with theoretical guarantees. Extensive evaluations on tasks including RL with noisy reward, BC with weak demonstrations, and standard policy co-training (RL + BC) show that the proposed approach leads to substantial improvements, especially when the complexity or the noise of the learning environments grows. 