We study the design of contests for specific innovations when there is learning: contestants’ beliefs dynamically evolve about both the innovation’s feasibility and opponents’ success. Our model builds on exponential-bandit experimentation. We characterize contests that maximize the probability of innovation when the designer chooses how to allocate a prize and what information to disclose over time about contestants’ successes. A “public winner-takes-all contest” dominates public contests—those where any success is immediately disclosed—with any other prize-sharing scheme as well as winner-takes-all contests with any other disclosure policy. Yet, it is often optimal to use a “hidden equal-sharing contest”.