How can we optimize for the Sharpe ratio if we only have limited training data? Estimates of mean asset returns are noisy, and this noise hurts the out-of-sample Sharpe ratio of current methods. The minimum-variance portfolio, which ignores mean returns, often has a better Sharpe ratio. We develop a parameter-free and scalable method called AlphaRob for this problem. AlphaRob ’s portfolio is a convex combination of two prespecified portfolios. To select the best combination, AlphaRob fuses robust optimization with a new notion of a portfolio’s regret that accounts for the training data’s size. Our analysis only needs mild assumptions on the distribution of asset returns. AlphaRob significantly outperforms competing methods on several simulated and real-world datasets, even after adjusting for transaction costs. AlphaRob is 7.5% better on average than the nearest competitor, and 28% better than the next-best combination portfolio method. Using our regret of regret, we are also able to explain the performance of the minimum-variance portfolio.