  This work proposes a framework for multistage adjustable robust optimization
that unifies the treatment of three different types of endogenous uncertainty,
where decisions, respectively, (i) alter the uncertainty set, (ii) affect the
materialization of uncertain parameters, and (iii) determine the time when the
true values of uncertain parameters are observed. We provide a systematic
analysis of the different types of endogenous uncertainty and highlight the
connection between optimization under endogenous uncertainty and active
learning. We consider decision-dependent polyhedral uncertainty sets and
propose a decision rule approach that incorporates both continuous and binary
recourse, including recourse decisions that affect the uncertainty set. The
proposed method enables the modeling of decision-dependent nonanticipativity
and results in a tractable reformulation of the problem. We demonstrate the
effectiveness of the approach in computational experiments that cover a range
of applications, including plant redesign, maintenance planning with
inspections, optimizing revision points in capacity planning, and production
scheduling with active parameter estimation. The results show significant
benefits from the proper modeling of endogenous uncertainty and active
learning.
