It can be difficult to predict market conditions, like consumer demand and production costs. Are there regulations, for monopolistic markets, that remain effective even when market conditions are unpredictable? Drawing from the literature on online optimization, I address this question using a new framework -- doubly robust mechanism design -- that relaxes prior knowledge for both the regulator and the firm. I find regulations that obtain meaningful and optimal welfare guarantees; they incentivize the firm to care about consumer surplus in addition to profits, but otherwise leave it with a free hand.