From experience, regulated monopolists learn to employ cost-reducing innovations. We characterize the optimal regulation of an innovating monopolist with unknown costs. Regulatory policy is designed to minimize current costs of service while encouraging development of cost-saving innovations. We find that under optimal regulation, (i) innovation is encouraged by light-handed regulation allowing the monopolist to earn greater information rents while providing greater service, (ii) innovation occurs in the absence of long-term agreements when private information is recurring, and (iii) innovation is more rapid in a durable franchise, and the regulator prefers durable franchises for exploiting learning economies.