Distributional Off-Policy Evaluation in Reinforcement Learning
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In the literature of reinforcement learning (RL), off-policy evaluation is mainly focused on estimating a value of a target policy given the pre-collected data generated by some behavior policy. Motivated by the recent success of distributional RL in many practical applications, we study the distributional off-policy evaluation problem in the batch setting when the reward is multi-variate. We propose an offline Wasserstein-based approach to simultaneously estimate the joint distribution of a multivariate discounted cumulative reward given any initial state-action pair in the setting of an infinite-horizon Markov decision process. Finite sample error bound for the proposed estimator with respect to a modified Wasserstein metric is established in terms of both the number of trajectories and the number of decision points on each trajectory in the batch data. Extensive numerical studies are conducted to demonstrate the superior performance of our proposed method.
Two frequent approaches for identifying structural VARs are external instruments, which carry economic content but are often weak, and non-Gaussianity of the shocks, which provides statistical identification but carries no economic meaning. We combine the two strategies in a single generalized method of moments framework. This hybrid approach point-identifies the target shocks while also identifying the non-target shocks up to sign and ordering. Under suitable rank…
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We study the role of design smoothness in the minimax estimation of conditional average treatment effects at a fixed covariate point. For design densities bounded above and away from zero, without further regularity, we derive upper and lower risk bounds with an arbitrarily small gap in the convergence-rate exponent. Under uniform design, we obtain matching upper and lower bounds at interior points in the regime of low nuisance smoothness. These results show that rough…
Bayesian additive regression trees (BART) is a popular Bayesian ensemble model used in regression and classification analysis. Under this modeling framework, the regression function is approximated by an ensemble of decision trees, interpreted as weak learners. In this work, we propose a generalization of the BART model that has two main features: first, it automatically selects the number of decision trees using the given data; second, the model allows clusters of…
估计纵向因果剂量反应关系的贝叶斯框架
Existing causal methods for time-varying exposure and time-varying confounding focus on estimating the average causal effect of a time-varying binary treatment on an end-of-study outcome, offering limited tools for characterizing marginal causal dose-response relationships under continuous exposures. We propose a scalable, nonparametric Bayesian framework for estimating marginal longitudinal causal dose-response functions with repeated outcome measurements. Our approach…
超越协方差的线性回归:高阶累积量中的潜在斜率谱
Least squares summarizes the joint distribution of a response and regressor through second-order information. When an observed regressor is composed of latent components carrying different relationships with the response, this summary can average over distinct linear effects. We study the additional linear information contained in higher-order mixed cumulants and formalize it through the latent slope spectrum. Ordinary least squares is a variance-weighted barycenter of this…
The conditional average treatment effect (CATE) is frequently estimated in clinical studies to refute a homogeneous treatment effect hypothesis. Under this regime, all patients making up the population experience identical benefit from a given treatment relative to a comparator. Uncovering heterogeneous treatment effects through inference about the CATE, however, requires that covariates truly modifying the treatment effect be reliably collected at baseline. CATE-based…