Computerized adaptive testing (CAT) is a central topic in item response theory. Its objective is to assign items adaptively so as to obtain accurate ability estimates with as few items as possible. A common implementation of CAT is based on the two-parameter logistic model, and among item-selection procedures, the best-known algorithm is Lord's information-maximization method, which selects the next item by maximizing Fisher information at the current ability estimate. Despite extensive research on the asymptotic properties of CAT algorithms, a comprehensive framework for understanding their behavior in finite samples is still absent. As a result, previous assessments of finite-sample performance have relied primarily on simulations, which lack sufficient theoretical support. This study addresses this gap by incorporating the online convex optimization framework into the CAT setting, with the goal of bridging the divide between finite-sample guarantees and asymptotic results. The research is organized around two complementary themes. The Precision theme focuses on developing theoretical tools to assess the finite-sample performance of CAT, with particular emphasis on constructing confidence intervals that rigorously quantify estimation uncertainty. The Robustness theme builds on these foundations to design stability-oriented adaptive testing algorithms that explicitly account for early-stage estimation error and potential model misspecification.