A main research goal in various studies is to use an observational data set
and provide a new set of counterfactual guidelines that can yield causal
improvements. Dynamic Treatment Regimes (DTRs) are widely studied to formalize
this process. However, available methods in finding optimal DTRs often rely on
assumptions that are violated in real-world applications (e.g., medical
decision-making or public policy), especially when (a) the existence of
unobserved confounders cannot be ignored, and (b) the unobserved confounders
are time-varying (e.g., affected by previous actions). When such assumptions
are violated, one often faces ambiguity regarding the underlying causal model.
This ambiguity is inevitable, since the dynamics of unobserved confounders and
their causal impact on the observed part of the data cannot be understood from
the observed data. Motivated by a case study of finding superior treatment
regimes for patients who underwent transplantation in our partner hospital and
faced a medical condition known as New Onset Diabetes After Transplantation
(NODAT), we extend DTRs to a new class termed Ambiguous Dynamic Treatment
Regimes (ADTRs), in which the causal impact of treatment regimes is evaluated
based on a "cloud" of causal models. We then connect ADTRs to Ambiguous
Partially Observable Mark Decision Processes (APOMDPs) and develop
Reinforcement Learning methods, which enable using the observed data to
efficiently learn an optimal treatment regime. We establish theoretical results
for these learning methods, including (weak) consistency and asymptotic
normality. We further evaluate the performance of these learning methods both
in our case study and in simulation experiments