Conversion rate optimization means designing web interfaces such that more visitors perform a desired action (such as register or purchase) on the site. One promising approach, implemented in Sentient Ascend, is to optimize the design using evolutionary algorithms, evaluating each candidate design online with actual visitors. Because such evaluations are costly and noisy, several challenges emerge: How can available visitor traffic be used most efficiently? How can good solutions be identified most reliably? How can a high conversion rate be maintained during optimization? This paper proposes a new technique to address these issues. Traffic is allocated to candidate solutions using a multi-armed bandit algorithm, using more traffic on those evaluations that are most useful. In a best-arm identification mode, the best candidate can be identified reliably at the end of evolution, and in a campaign mode, the overall conversion rate can be optimized throughout the entire evolution process. Multi-armed bandit algorithms thus improve performance and reliability of machine discovery in noisy real-world environments.