Doubly robust uncertainty quantification for quantile treatment effects in sequential decision making

We consider multi-stage sequential decision making, where the treatment at any stage may depend on the subject’s entire treatment and covariate history. We introduce a general framework for doubly robust uncertainty quantification for the quantiles of cumulative outcomes under a sequential treatment rule. While previous studies focused on mean effects, quantile effects offer unique insights into the distributional properties and are more robust for heavytailed outcomes. It is known that, doubly robust inference is significantly more challenging and largely unexplored for quantile treatment effects. More importantly, for mean effects, doubly robust estimation does not ensure doubly robust inference. Our approach first provides a doubly robust estimator for any quantile of interest based on pre-collected data, achieving semi-parametric efficiency. We then propose a novel doubly robust estimator for the asymptotic variance, enabling the construction of a doubly robust confidence interval. To overcome the challenges in parameter-dependent nuisance functions, we leverage deep conditional generative learning techniques. We demonstrate advantages of our approach via both simulation and real data from a short video platform. Additionally, we observe that our proposed approach leads to another mean effect estimator that outperforms existing estimators with heavy-tailed outcomes.