Solving real-world stochastic optimization problems (e.g., in machine learning) presents two key challenges: the messiness of real-world data, which can be noisy, biased, or corrupted due to factors like outliers, distribution shifts, and even adversarial attacks; and the laborious, time-intensive requirement of manually tuning step sizes in many existing algorithms. I study stochastic adaptive optimization algorithms under a simple, common framework. The algorithms in this framework avoid the need for manual step size tuning by adaptively adjusting it in each iteration based on the algorithm's progress. To address the issue of messy data, the framework only assumes access to function-related information through probabilistic oracles, which may be biased and corrupted. This framework is very general, encompassing a wide range of algorithms, and is applicable to multiple problem settings, such as expected loss minimization in machine learning, simulation optimization, and derivative-free optimization. We establish iteration complexity bounds for two algorithms within it — stochastic adaptive step search and stochastic adaptive cubic-regularized Newton method — under reasonable oracle conditions. Additionally, we derive a meta-theorem to bound the sample complexity for any algorithm in the framework.