This paper introduces a novel multiagent learning algorithm, Convergence with Model Learning and Safety (or CMLeS in short), which achieves convergence, targeted optimality against memory-bounded adversaries, and safety, in arbitrary repeated games. The most novel aspect of CMLeS is the manner in which it guarantees (in a PAC sense) targeted optimality against memory-bounded adversaries, via efficient exploration and exploitation. CMLeS is fully implemented and we present empirical results demonstrating its effectiveness.