  Controllable learning (CL) emerges as a critical component in trustworthy
machine learning, ensuring that learners meet predefined targets and can
adaptively adjust without retraining according to the changes in those targets.
We provide a formal definition of CL, and discuss its applications in
information retrieval (IR) where information needs are often complex and
dynamic. The survey categorizes CL according to who controls (users or
platforms), what is controllable (e.g., retrieval objectives, users' historical
behaviors, controllable environmental adaptation), how control is implemented
(e.g., rule-based method, Pareto optimization, Hypernetwork), and where to
implement control (e.g.,pre-processing, in-processing, post-processing
methods). Then, we identify challenges faced by CL across training, evaluation,
task setting, and deployment in online environments. Additionally, we outline
promising directions for CL in theoretical analysis, efficient computation,
empowering large language models, application scenarios and evaluation
frameworks in IR.
