Semiparametric Double Reinforcement Learning with Applications to Long-Term Causal Inference

• URL: http://arxiv.org/abs/2501.06926v3
• Date: Mon, 30 Jun 2025 16:30:42 GMT
• Title: Semiparametric Double Reinforcement Learning with Applications to Long-Term Causal Inference
• Authors: Lars van der Laan, David Hubbard, Allen Tran, Nathan Kallus, Aurélien Bibaut,
• Abstract summary: Long-term causal effects must be estimated from short-term data.<n>MDPs provide a natural framework for capturing such long-term dynamics.<n>Nonparametric implementations require strong intertemporal overlap assumptions.<n>We introduce a novel plug-in estimator based on isotonic Bellman calibration.
• Score: 33.14076284663493
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Long-term causal effects often must be estimated from short-term data due to limited follow-up in healthcare, economics, and online platforms. Markov Decision Processes (MDPs) provide a natural framework for capturing such long-term dynamics through sequences of states, actions, and rewards. Double Reinforcement Learning (DRL) enables efficient inference on policy values in MDPs, but nonparametric implementations require strong intertemporal overlap assumptions and often exhibit high variance and instability. We propose a semiparametric extension of DRL for efficient inference on linear functionals of the Q-function--such as policy values--in infinite-horizon, time-homogeneous MDPs. By imposing structural restrictions on the Q-function, our approach relaxes the strong overlap conditions required by nonparametric methods and improves statistical efficiency. Under model misspecification, our estimators target the functional of the best-approximating Q-function, with only second-order bias. We provide conditions for valid inference using sieve methods and data-driven model selection. A central challenge in DRL is the estimation of nuisance functions, such as density ratios, which often involve difficult minimax optimization. To address this, we introduce a novel plug-in estimator based on isotonic Bellman calibration, which combines fitted Q-iteration with an isotonic regression adjustment. The estimator is debiased without requiring estimation of additional nuisance functions and reduces high-dimensional overlap assumptions to a one-dimensional condition. Bellman calibration extends isotonic calibration--widely used in prediction and classification--to the MDP setting and may be of independent interest.

Related papers

• Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update [60.414548453838506]
  We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function.<n>GLBs are widely applicable to real-world scenarios, but their non-linear nature introduces significant challenges in achieving both computational and statistical efficiency.<n>We propose a jointly efficient algorithm that attains a nearly optimal regret bound with $mathcalO(1)$ time and space complexities per round.
  arXiv  Detail & Related papers  (2025-07-16T02:24:21Z)
• Principled Input-Output-Conditioned Post-Hoc Uncertainty Estimation for Regression Networks [1.4671424999873808]
  Uncertainty is critical in safety-sensitive applications but is often omitted from off-the-shelf neural networks due to adverse effects on predictive performance.<n>We propose a theoretically grounded framework for post-hoc uncertainty estimation in regression tasks by fitting an auxiliary model to both original inputs and frozen model outputs.
  arXiv  Detail & Related papers  (2025-06-01T09:13:27Z)
• Debiased Ill-Posed Regression [8.495265117285223]
  We propose a debiased estimation strategy based on the influence function of a modification of the projected error.<n>Our proposed estimator possesses a second-order bias with respect to the involved nuisance functions.
  arXiv  Detail & Related papers  (2025-05-27T06:47:33Z)
• Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands [34.30497962430375]
  We propose a unified framework for automatic debiased machine learning (autoDML) to perform inference on smooth functionals of infinite-dimensional M-estimands. We introduce three autoDML estimators based on one-step estimation, targeted minimum loss-based estimation, and the method of sieves. For data-driven model selection, we derive a novel decomposition of model approximation error for smooth functionals of M-estimands.
  arXiv  Detail & Related papers  (2025-01-21T03:50:51Z)
• Semiparametric inference for impulse response functions using double/debiased machine learning [49.1574468325115]
  We introduce a machine learning estimator for the impulse response function (IRF) in settings where a time series of interest is subjected to multiple discrete treatments. The proposed estimator can rely on fully nonparametric relations between treatment and outcome variables, opening up the possibility to use flexible machine learning approaches to estimate IRFs.
  arXiv  Detail & Related papers  (2024-11-15T07:42:02Z)
• Automatic doubly robust inference for linear functionals via calibrated debiased machine learning [0.9694940903078658]
  We propose a debiased machine learning estimator for doubly robust inference. A C-DML estimator maintains linearity when either the outcome regression or the Riesz representer of the linear functional is estimated sufficiently well. Our theoretical and empirical results support the use of C-DML to mitigate bias arising from the inconsistent or slow estimation of nuisance functions.
  arXiv  Detail & Related papers  (2024-11-05T03:32:30Z)
• Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise [51.87307904567702]
  Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the distribution of outputs.<n>We propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint.<n>We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities.
  arXiv  Detail & Related papers  (2024-06-05T13:36:38Z)
• Efficient and Sharp Off-Policy Evaluation in Robust Markov Decision Processes [44.974100402600165]
  We study the evaluation of a policy best-parametric and worst-case perturbations to a decision process (MDP) We use transition observations from the original MDP, whether they are generated under the same or a different policy. Our estimator is also estimated statistical inference using Wald confidence intervals.
  arXiv  Detail & Related papers  (2024-03-29T18:11:49Z)
• Online non-parametric likelihood-ratio estimation by Pearson-divergence functional minimization [55.98760097296213]
  We introduce a new framework for online non-parametric LRE (OLRE) for the setting where pairs of iid observations $(x_t sim p, x'_t sim q)$ are observed over time. We provide theoretical guarantees for the performance of the OLRE method along with empirical validation in synthetic experiments.
  arXiv  Detail & Related papers  (2023-11-03T13:20:11Z)
• FAStEN: An Efficient Adaptive Method for Feature Selection and Estimation in High-Dimensional Functional Regressions [7.674715791336311]
  We propose a new, flexible and ultra-efficient approach to perform feature selection in a sparse function-on-function regression problem. We show how to extend it to the scalar-on-function framework. We present an application to brain fMRI data from the AOMIC PIOP1 study.
  arXiv  Detail & Related papers  (2023-03-26T19:41:17Z)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes [80.89852729380425]
  We propose the first computationally efficient algorithm that achieves the nearly minimax optimal regret $tilde O(dsqrtH3K)$. Our work provides a complete answer to optimal RL with linear MDPs, and the developed algorithm and theoretical tools may be of independent interest.
  arXiv  Detail & Related papers  (2022-12-12T18:58:59Z)
• GEC: A Unified Framework for Interactive Decision Making in MDP, POMDP, and Beyond [101.5329678997916]
  We study sample efficient reinforcement learning (RL) under the general framework of interactive decision making. We propose a novel complexity measure, generalized eluder coefficient (GEC), which characterizes the fundamental tradeoff between exploration and exploitation. We show that RL problems with low GEC form a remarkably rich class, which subsumes low Bellman eluder dimension problems, bilinear class, low witness rank problems, PO-bilinear class, and generalized regular PSR.
  arXiv  Detail & Related papers  (2022-11-03T16:42:40Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Solving Multistage Stochastic Linear Programming via Regularized Linear Decision Rules: An Application to Hydrothermal Dispatch Planning [77.34726150561087]
  We propose a novel regularization scheme for linear decision rules (LDR) based on the AdaSO (adaptive least absolute shrinkage and selection operator) Experiments show that the overfit threat is non-negligible when using the classical non-regularized LDR to solve MSLP. For the LHDP problem, our analysis highlights the following benefits of the proposed framework in comparison to the non-regularized benchmark.
  arXiv  Detail & Related papers  (2021-10-07T02:36:14Z)
• Implicitly Regularized RL with Implicit Q-Values [42.87920755961722]
  The $Q$-function is a central quantity in many Reinforcement Learning (RL) algorithms for which RL agents behave following a (soft)-greedy policy. We propose to parametrize the $Q$-function implicitly, as the sum of a log-policy and of a value function. We derive a practical off-policy deep RL algorithm, suitable for large action spaces, and that enforces the softmax relation between the policy and the $Q$-value.
  arXiv  Detail & Related papers  (2021-08-16T12:20:47Z)
• Learning MDPs from Features: Predict-Then-Optimize for Sequential Decision Problems by Reinforcement Learning [52.74071439183113]
  We study the predict-then-optimize framework in the context of sequential decision problems (formulated as MDPs) solved via reinforcement learning. Two significant computational challenges arise in applying decision-focused learning to MDPs.
  arXiv  Detail & Related papers  (2021-06-06T23:53:31Z)
• Exploiting Submodular Value Functions For Scaling Up Active Perception [60.81276437097671]
  In active perception tasks, agent aims to select sensory actions that reduce uncertainty about one or more hidden variables. Partially observable Markov decision processes (POMDPs) provide a natural model for such problems. As the number of sensors available to the agent grows, the computational cost of POMDP planning grows exponentially.
  arXiv  Detail & Related papers  (2020-09-21T09:11:36Z)
• Fundamental Limits of Ridge-Regularized Empirical Risk Minimization in High Dimensions [41.7567932118769]
  Empirical Risk Minimization algorithms are widely used in a variety of estimation and prediction tasks. In this paper, we characterize for the first time the fundamental limits on the statistical accuracy of convex ERM for inference.
  arXiv  Detail & Related papers  (2020-06-16T04:27:38Z)
• Learning Stable Nonparametric Dynamical Systems with Gaussian Process Regression [9.126353101382607]
  We learn a nonparametric Lyapunov function based on Gaussian process regression from data. We prove that stabilization of the nominal model based on the nonparametric control Lyapunov function does not modify the behavior of the nominal model at training samples.
  arXiv  Detail & Related papers  (2020-06-14T11:17:17Z)
• Machine learning for causal inference: on the use of cross-fit estimators [77.34726150561087]
  Doubly-robust cross-fit estimators have been proposed to yield better statistical properties. We conducted a simulation study to assess the performance of several estimators for the average causal effect (ACE) When used with machine learning, the doubly-robust cross-fit estimators substantially outperformed all of the other estimators in terms of bias, variance, and confidence interval coverage.
  arXiv  Detail & Related papers  (2020-04-21T23:09:55Z)
• Minimax-Optimal Off-Policy Evaluation with Linear Function Approximation [49.502277468627035]
  This paper studies the statistical theory of batch data reinforcement learning with function approximation. Consider the off-policy evaluation problem, which is to estimate the cumulative value of a new target policy from logged history.
  arXiv  Detail & Related papers  (2020-02-21T19:20:57Z)
• Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond [69.83813153444115]
  We consider an efficient estimating equation for the (local) quantile treatment effect ((L)QTE) in causal inference. Debiased machine learning (DML) is a data-splitting approach to estimating high-dimensional nuisances. We propose localized debiased machine learning (LDML), which avoids this burdensome step.
  arXiv  Detail & Related papers  (2019-12-30T14:42:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.