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Register a new userCausal Reinforcement Learning: An Instrumental Variable Approach
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In the standard data analysis framework, data is first collected (once for all), and then data analysis is carried out. With the advancement of digital technology, decisionmakers constantly analyze past data and generate new data through the decisions they make. In this paper, we model this as a Markov decision process and show that the dynamic interaction between data generation and data analysis leads to a new type of bias -- reinforcement bias -- that exacerbates the endogeneity problem in standard data analysis. We propose a class of instrument variable (IV)-based reinforcement learning (RL) algorithms to correct for the bias and establish their asymptotic properties by incorporating them into a two-timescale stochastic approximation framework. A key contribution of the paper is the development of new techniques that allow for the analysis of the algorithms in general settings where noises feature time-dependency. We use the techniques to derive sharper results on finite-time trajectory stability bounds: with a polynomial rate, the entire future trajectory of the iterates from the algorithm fall within a ball that is centered at the true parameter and is shrinking at a (different) polynomial rate. We also use the technique to provide formulas for inferences that are rarely done for RL algorithms. These formulas highlight how the strength of the IV and the degree of the noises time dependency affect the inference.
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Most existing studies on the double/debiased machine learning method concentrate on the causal parameter estimation recovering from the first-order orthogonal score function. In this paper, we will construct the $k^{mathrm{th}}$-order orthogonal score function for estimating the average treatment effect (ATE) and present an algorithm that enables us to obtain the debiased estimator recovered from the score function. Such a higher-order orthogonal estimator is more robust to the misspecification of the propensity score than the first-order one does. Besides, it has the merit of being applicable with many machine learning methodologies such as Lasso, Random Forests, Neural Nets, etc. We also undergo comprehensive experiments to test the power of the estimator we construct from the score function using both the simulated datasets and the real datasets.
The inference of causal relationships using observational data from partially observed multivariate systems with hidden variables is a fundamental question in many scientific domains. Methods extracting causal information from conditional independencies between variables of a system are common tools for this purpose, but are limited in the lack of independencies. To surmount this limitation, we capitalize on the fact that the laws governing the generative mechanisms of a system often result in substructures embodied in the generative functional equation of a variable, which act as sufficient statistics for the influence that other variables have on it. These functional sufficient statistics constitute intermediate hidden variables providing new conditional independencies to be tested. We propose to use the Information Bottleneck method, a technique commonly applied for dimensionality reduction, to find underlying sufficient sets of statistics. Using these statistics we formulate new additional rules of causal orientation that provide causal information not obtainable from standard structure learning algorithms, which exploit only conditional independencies between observable variables. We validate the use of sufficient statistics for structure learning both with simulated systems built to contain specific sufficient statistics and with benchmark data from regulatory rules previously and independently proposed to model biological signal transduction networks.
Estimating dynamic treatment regimes (DTRs) from retrospective observational data is challenging as some degree of unmeasured confounding is often expected. In this work, we develop a framework of estimating properly defined optimal DTRs with a time-varying instrumental variable (IV) when unmeasured covariates confound the treatment and outcome, rendering the potential outcome distributions only partially identified. We derive a novel Bellman equation under partial identification, use it to define a generic class of estimands (termed IV-optimal DTRs), and study the associated estimation problem. We then extend the IV-optimality framework to tackle the policy improvement problem, delivering IV-improved DTRs that are guaranteed to perform no worse and potentially better than a pre-specified baseline DTR. Importantly, our IV-improvement framework opens up the possibility of strictly improving upon DTRs that are optimal under the no unmeasured confounding assumption (NUCA). We demonstrate via extensive simulations the superior performance of IV-optimal and IV-improved DTRs over the DTRs that are optimal only under the NUCA. In a real data example, we embed retrospective observational registry data into a natural, two-stage experiment with noncompliance using a time-varying IV and estimate useful IV-optimal DTRs that assign mothers to high-level or low-level neonatal intensive care units based on their prognostic variables.
The R package DoubleML implements the double/debiased machine learning framework of Chernozhukov et al. (2018). It provides functionalities to estimate parameters in causal models based on machine learning methods. The double machine learning framework consist of three key ingredients: Neyman orthogonality, high-quality machine learning estimation and sample splitting. Estimation of nuisance components can be performed by various state-of-the-art machine learning methods that are available in the mlr3 ecosystem. DoubleML makes it possible to perform inference in a variety of causal models, including partially linear and interactive regression models and their extensions to instrumental variable estimation. The object-oriented implementation of DoubleML enables a high flexibility for the model specification and makes it easily extendable. This paper serves as an introduction to the double machine learning framework and the R package DoubleML. In reproducible code examples with simulated and real data sets, we demonstrate how DoubleML users can perform valid inference based on machine learning methods.
DoubleML is an open-source Python library implementing the double machine learning framework of Chernozhukov et al. (2018) for a variety of causal models. It contains functionalities for valid statistical inference on causal parameters when the estimation of nuisance parameters is based on machine learning methods. The object-oriented implementation of DoubleML provides a high flexibility in terms of model specifications and makes it easily extendable. The package is distributed under the MIT license and relies on core libraries from the scientific Python ecosystem: scikit-learn, numpy, pandas, scipy, statsmodels and joblib. Source code, documentation and an extensive user guide can be found at https://github.com/DoubleML/doubleml-for-py and https://docs.doubleml.org.
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