  We consider the estimation of treatment effects in settings when multiple
treatments are assigned over time and treatments can have a causal effect on
future outcomes or the state of the treated unit. We propose an extension of
the double/debiased machine learning framework to estimate the dynamic effects
of treatments, which can be viewed as a Neyman orthogonal (locally robust)
cross-fitted version of $g$-estimation in the dynamic treatment regime. Our
method applies to a general class of non-linear dynamic treatment models known
as Structural Nested Mean Models and allows the use of machine learning methods
to control for potentially high dimensional state variables, subject to a mean
square error guarantee, while still allowing parametric estimation and
construction of confidence intervals for the structural parameters of interest.
These structural parameters can be used for off-policy evaluation of any target
dynamic policy at parametric rates, subject to semi-parametric restrictions on
the data generating process. Our work is based on a recursive peeling process,
typical in $g$-estimation, and formulates a strongly convex objective at each
stage, which allows us to extend the $g$-estimation framework in multiple
directions: i) to provide finite sample guarantees, ii) to estimate non-linear
effect heterogeneity with respect to fixed unit characteristics, within
arbitrary function spaces, enabling a dynamic analogue of the RLearner
algorithm for heterogeneous effects, iii) to allow for high-dimensional sparse
parameterizations of the target structural functions, enabling automated model
selection via a recursive lasso algorithm. We also provide guarantees for data
stemming from a single treated unit over a long horizon and under stationarity
conditions.
