Before revision:  We prove the exploitability estimation error bounds for OPE and regret bounds for OPL based on the doubly robust and double reinforcement learning estimators .
After revision:  We prove the exploitability estimation error bounds for the proposed estimators. We then propose the methods to find the best candidate policy profile by selecting the policy profile that minimizes the estimated exploitability from a given policy profile class. We prove the regret bounds of the policy profiles selected by our methods .