In learn-as-you-go (LAGO) adaptive studies, the intervention is a complex package consisting of multiple components, and is adapted in stages during the study based on past outcome data. This design formalizes standard practice, and desires for practice, in public health intervention studies. An effective intervention package is sought, while minimizing intervention package cost. Here, the recommended interventions in later stages depend upon the outcomes in the previous stages, violating the standard statistical theory. We develop a methods for estimating the intervention effects in a LAGO study. We prove consistency and asymptotic normality using a novel coupling argument, ensuring the validity of the test for the hypothesis of no overall intervention effect. We further develop a confidence set for the optimal intervention package and confidence bands for the success probabilities under different alternative package compositions. We illustrate our methods in the BetterBirth Study, which aimed to improve maternal and neonatal outcomes among 157,689 births in Uttar Pradesh, India through a complex, multi-component intervention package.