arXiv subjects

Lars van der Laan

Publications and source records attributed to Lars van der Laan.

At least 19 recordsLinked to original sources

arXiv2026

Fitted Q-Evaluation without Bellman Completeness via Occupancy Weighting

Fitted $Q$-evaluation (FQE) is a standard regression-based method for off-policy evaluation, but under distribution shift, value-function realizability alone does not ensure convergence, and existing analyses often require Bellman completeness. We trace this instability to a geometric mismatch: standard FQE projects Bellman targets in the norm induced by the offline distribution, which need not preserve Bellman contraction. We therefore study \emph{occupancy-weighted FQE}, which changes only the regression weights. Weighting by a target-policy discounted occupancy ratio aligns the projection norm with the target-policy dynamics and restores contraction of the population projected Bellman operator. We derive finite-sample guarantees with estimated occupancy ratios and function-class misspecification, separating finite-iteration, statistical, approximation, and ratio-estimation errors. Exact occupancy weighting removes the need for Bellman completeness; with estimated weights, approximate completeness and value-function realizability reduce sensitivity to ratio-estimation error, with exact realizability yielding higher-order dependence. Combining occupancy-weighted FQE with fitted occupancy-ratio evaluation gives an end-to-end guarantee governed by the complexities and direct approximation errors of the value-function and occupancy-ratio classes. Under coverage, joint realizability of these two classes suffices for consistent estimation without Bellman or critic-side completeness. Controlled experiments illustrate the projection-norm mechanism and the finite-sample tradeoff between contraction and coverage.

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arXiv2026

Soft Fitted Q-Iteration without Bellman Completeness: Occupancy Reweighting and Temperature Annealing

Fitted $Q$-iteration (FQI) is a standard regression-based method for optimal control in offline reinforcement learning, but its stability under function approximation often relies on Bellman completeness, which requires Bellman images of the fitted class to remain in the class. We study Kullback--Leibler (KL)-regularized, or soft, FQI relative to a fixed reference policy without this assumption. Our key insight is that soft control locally inherits the contraction of policy evaluation in a discounted-occupancy norm. At the soft-optimal fixed point, the linearization of the soft Bellman operator is exactly the Bellman operator for the soft-optimal policy, which contracts in its discounted-occupancy norm; projection in the same norm preserves this contraction. Standard soft FQI instead projects under the offline state-action distribution and need not preserve this property. Motivated by this observation, we propose \emph{occupancy-reweighted soft FQI}, which retains standard Bellman targets and least-squares updates while reweighting regressions by discounted-occupancy ratios induced by the current soft policy. Under $Q$-function realizability and local regularity, we establish local contraction and finite-sample convergence with estimated ratios, without Bellman completeness. We then use temperature annealing to convert the local result into global convergence from arbitrary initialization: sufficiently high temperature provides a globally contractive starting regime, while gradual cooling connects successive local contraction regions to any prescribed positive target temperature. Under an action-gap margin condition, switching at a fixed positive temperature to hard FQI with refreshed occupancy weights also yields population and finite-sample convergence to the unregularized optimum.

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arXiv2026

Bellman Calibration for Marginalized Importance Weighting in Offline Reinforcement Learning

Marginalized importance weighting evaluates a target policy by reweighting offline state-action samples with its discounted occupancy ratio, characterized by an adjoint Bellman equation. Existing minimax, primal-dual, and fitted fixed-point estimators can leave residual occupancy-balance violations because of function-class approximation, regularization, or incomplete optimization. These violations are difficult to diagnose and reduce because the objectives generally lack a direct supervised validation loss for hyperparameter tuning, model selection, and early stopping. We introduce isotonic Bellman calibration, a one-dimensional, model-agnostic post-processing method that reduces these violations while preserving the ranking information in any initial occupancy-ratio estimate. The method corrects the estimate's scale and shape by applying fitted occupancy-ratio evaluation (FORE) over a one-dimensional class of nondecreasing transformations. We characterize Bellman calibration as a conditional fixed-point property equivalent to occupancy-balance against every test function of the calibrated ratio. More generally, we derive a calibration-refinement bound showing that any fitted ratio with small calibration error performs nearly as well as the best post-processing based on its fitted values. For isotonic Bellman calibration, we establish finite-sample calibration guarantees and a KL oracle inequality relative to the best monotone transformation of the initial estimate. Consequently, isotonic Bellman calibration achieves small calibration error and KL risk within statistical error of the best monotone correction, with guarantees for downstream target-occupancy functionals, including policy-value estimation.

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arXiv2026

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

Double reinforcement learning (DRL) provides efficient off-policy inference for policy values in nonparametric Markov decision processes (MDPs), but fully nonparametric estimators can be unstable when intertemporal overlap is weak and occupancy ratios are high-dimensional. This limitation is especially relevant for long-term causal inference from randomized experiments: randomization ensures overlap in treatment assignment, but not over future state trajectories induced by continued intervention use. We develop semiparametric DRL for continuous linear functionals of the infinite-horizon $Q$-function. Rather than impose linear MDP structure on the reward and transition laws, we place working semiparametric restrictions on the $Q$-function itself, the solution of the discounted Bellman equation. When correct, these restrictions can improve efficiency relative to unrestricted DRL while allowing rich, possibly infinite-dimensional models. To avoid relying on correct specification, we define the estimand through weighted Bellman-residual minimization. The resulting projection target remains meaningful under misspecification and recovers the original functional under correct specification. For this class of parameters, we derive efficient influence functions and efficiency bounds, construct model-robust automatically debiased estimators, and develop minimax criteria for estimating the $Q$- and Riesz functions. Under correct specification, optimally weighted versions attain the semiparametric efficiency bound in the restricted model.

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arXiv2026

Doubly robust inference via calibration

Doubly robust estimators are widely used for estimating average treatment effects and other linear summaries of regression functions. While consistency requires only one of two nuisance functions to be estimated consistently, asymptotic normality for linear functionals typically requires sufficiently fast convergence of both. We address this mismatch by showing that calibrating the nuisance estimators within a doubly robust procedure can yield doubly robust asymptotic normality. We introduce the idea of calibrated debiased machine learning (DML) and propose a specific implementation in which standard DML is augmented with a simple isotonic regression adjustment. We show that, under a partial orthogonality condition, a calibrated DML estimator remains asymptotically normal if either the regression function or Riesz representer of the functional is estimated sufficiently well, allowing the other to converge arbitrarily slowly or even inconsistently. We also propose a bootstrap-assisted method for constructing confidence intervals, enabling doubly robust inference without additional nuisance estimation. In a range of semi-synthetic benchmark datasets, calibrated DML reduces bias and improves coverage relative to standard DML. Our method can be integrated into existing DML pipelines by adding just a few lines of code to calibrate cross-fitted estimates via isotonic regression.

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arXiv2026

Efficient Inference for Inverse Reinforcement Learning and Dynamic Discrete Choice Models

In many sequential decision-making problems, researchers observe actions but not the rewards that drive behavior, yet still wish to evaluate and compare counterfactual policies. Inverse reinforcement learning (IRL) and dynamic discrete choice (DDC) models address this setting by positing an optimality model that links latent rewards to observed actions. Existing flexible IRL methods allow rich reward representations but typically do not provide valid inference, whereas classical DDC methods support inference only under restrictive parametric structure. We develop a semiparametric framework for debiased inverse reinforcement learning in maximum-entropy IRL and Gumbel-shock DDC models. Our key identification result is that the log-behavior policy can be treated as a pseudo-reward: it point-identifies policy value differences and, under a normalization constraint, the reward itself. This reduces inference on reward-dependent estimands to inference on smooth functionals of the behavior policy and transition kernel. We establish pathwise differentiability, derive efficient influence functions, and construct automatic debiased machine-learning estimators that permit flexible nuisance estimation while attaining $\sqrt{n}$-consistency, asymptotic normality, and semiparametric efficiency. The result is a computationally tractable framework for valid uncertainty quantification in flexible IRL and DDC models.

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arXiv2026

Fitted Occupancy-Ratio Evaluation without Bellman Completeness

Occupancy ratios correct distribution shift in offline reinforcement learning and are central to off-policy evaluation. Existing primal-dual and minimax methods typically estimate these ratios by enforcing occupancy-balance moments over a critic class. We propose fitted occupancy-ratio evaluation (FORE), a fitted fixed-point method that characterizes the discounted occupancy ratio through an adjoint Bellman recursion. At each iteration, FORE solves a single-level density-ratio objective on one-step-transition data, thereby projecting the adjoint Bellman image onto a log-ratio class in Kullback-Leibler (KL) divergence. Unlike analyses of fitted Q-evaluation, which typically require value-function realizability together with Bellman completeness or projected-operator stability, our central approximation condition is just realizability of the discounted occupancy ratio itself. Under this condition, the population KL-projected recursion contracts in relative entropy toward the true ratio by virtue of the adjoint Bellman operator being a KL-contraction. For the empirical recursion, we establish finite-sample regret bounds that yield convergence in KL up to approximation error and a statistical error governed by the complexity of the ratio hypothesis class. When full coverage fails, we introduce coverage-stopped FORE, which targets the discounted occupancy accumulated before the first uncovered state-action pair and yields a conservative lower bound on target-policy value for nonnegative rewards. The fitted ratio supports direct value estimation by reward reweighting, occupancy-weighted fitted Q-evaluation, and doubly robust estimation that combines the fitted ratio with a fitted Q-function. Together, these results identify discounted occupancy-ratio realizability as a sufficient condition for offline policy evaluation without any completeness assumptions.

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arXiv2026

Reward Transfer from Inverse Reinforcement Learning: A Coupled Minimax Approach

We study the transfer of rewards learned using inverse reinforcement learning from expert demonstrations in one environment to reinforcement learning in a new, different environment. This arises naturally when demonstrations are collected in a controlled environment. We formulate the problem as a joint system of Bellman equations across the source and target environments and develop minimax estimators for the target soft-$q$-function. Whereas a sequential solution approach first estimates the source reward and then plugs it into the target control problem, a coupled approach solves the source and target system of equations jointly. We show that, in contrast to the sequential approach, the coupled approach removes the first-order influence of source Bellman residual error. We characterize the local behavior of each approach, develop finite-sample soft-$q$-function error bounds, and prove regret guarantees for the resulting soft-control policy. An empirical investigation using a sepsis simulator validates the theoretical comparison.

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arXiv2026

Targeted maximum likelihood estimation of vaccine effectiveness and immune correlates in test-negative design studies with missing data

The test-negative design (TND) is a resource-efficient observational study design that can assess vaccine effectiveness and exposure-proximal immune correlates of disease. The TND enrolls symptomatic individuals seeking diagnostic testing and compares case status by an exposure variable, such as vaccination status or immune marker level, that is measured at testing. While the TND reduces confounding by healthcare-seeking behavior, other sources of confounding may remain. TND studies may also have missing data in the exposure variable due to incomplete records or two-phase sampling designs. We present a targeted maximum likelihood estimation approach involving a semiparametric logistic regression model that targets a causal conditional risk ratio of symptomatic disease in the healthcare-seeking population. Under causal and missing at random assumptions, our method produces an efficient, asymptotically linear estimator that provides flexible, data-driven confounding control and valid causal inference when analyzing TND studies with missing exposure variable data. We evaluate our method's finite sample properties using plasmode simulations of a two-phase TND immune correlates study. We also apply our method to assess COVID-19 vaccine effectiveness and antibody marker correlates of COVID-19 from TND study cohorts derived from the Moderna Coronavirus Efficacy phase 3 trial.

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arXiv2026

Inverse Reinforcement Learning with Just Classification and a Few Regressions

Inverse reinforcement learning (IRL) aims to infer rewards from observed behavior, but rewards are not identified from the policy alone: many reward--value pairs can rationalize the same actions. Meaningful reward recovery therefore requires a normalization, yet existing normalized IRL methods often rely on anchor-action restrictions or specialized neural architectures. We study reward recovery in the maximum-entropy, or Gumbel-shock, model under a broad class of statewise affine normalizations, with anchor-action constraints as a special case. This yields Generalized Policy-to-$Q$-to-Reward (GenPQR), a modular procedure that estimates the behavior policy, evaluates its soft $Q$-function through the Bellman equation, and recovers the normalized reward. Both stages can be implemented with off-the-shelf classification and regression methods. We prove modular finite-sample guarantees under general function approximation, with separate policy-estimation and $Q$-estimation errors. As a concrete instantiation, we study GenPQR with fitted $Q$-evaluation, reducing IRL to policy estimation followed by regression. Experiments show that GenPQR matches or improves reward recovery relative to DeepPQR while remaining simpler and more modular. Compared with DeepPQR, our theory goes beyond anchor actions, accommodates large and continuous action spaces, makes coverage requirements explicit, and is not tied to a specific neural-network architecture or training procedure.

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arXiv2026

Bellman Calibration for $V$-Learning in Offline Reinforcement Learning

Reliable long-horizon value prediction is difficult in offline reinforcement learning because fitted value methods combine bootstrapping, function approximation, and distribution shift, while standard guarantees often require Bellman completeness or realizability. We introduce Bellman calibration, a weak reliability criterion requiring that states assigned similar predicted values have average Bellman targets that agree with those predictions. This criterion yields a scalar calibration error for diagnosing systematic numerical miscalibration, which we estimate from off-policy data using doubly robust Bellman target estimates. We then propose Iterated Bellman Calibration, a model-agnostic post-hoc procedure that recalibrates any learned value predictor by fitting a one-dimensional map of its original prediction, with histogram and isotonic variants. We prove finite-sample guarantees showing that Bellman calibration error is controlled at one-dimensional nonparametric rates without Bellman completeness or value-function realizability. Our value-error bounds separate statistical estimation, finite-iteration, and approximation errors, clarifying when calibration improves value prediction and when its gains are limited by the information in the original predictor or insufficient coverage.

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arXiv2026

Calibeating Prediction-Powered Inference

We study semisupervised mean estimation with a small labeled sample, a large unlabeled sample, and a black-box prediction model whose output may be miscalibrated. A standard approach in this setting is augmented inverse-probability weighting (AIPW) [Robins et al., 1994], which protects against prediction-model misspecification but can be inefficient when the prediction score is poorly aligned with the outcome scale. We introduce Calibrated Prediction-Powered Inference, which post-hoc calibrates the prediction score on the labeled sample before using it for semisupervised estimation. This simple step requires no retraining and can improve the original score both as a predictor of the outcome and as a regression adjustment for semisupervised inference. We study both linear and isotonic calibration. For isotonic calibration, we establish first-order optimality guarantees: isotonic post-processing can improve predictive accuracy and estimator efficiency relative to the original score and simpler post-processing rules, while no further post-processing of the fitted isotonic score yields additional first-order gains. For linear calibration, we show first-order equivalence to PPI++. We also clarify the relationship among existing estimators, showing that the original PPI estimator is a special case of AIPW and can be inefficient when the prediction model is accurate, while PPI++ is AIPW with empirical efficiency maximization [Rubin et al., 2008]. In simulations and real-data experiments, our calibrated estimators often outperform PPI and are competitive with, or outperform, AIPW and PPI++. We provide an accompanying Python package, ppi_aipw, at https://larsvanderlaan.github.io/ppi-aipw/.

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arXiv2026

Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands

We develop a unified framework for automatic debiased machine learning (autoDML) for inference on a broad class of statistical parameters. The framework applies to any smooth functional of a nonparametric M-estimand, defined as the minimizer of a population risk over an infinite-dimensional linear space. Examples include counterfactual regression, quantile, and survival functions, as well as conditional average treatment effects. Rather than requiring manual derivation of influence functions, our approach automates the construction of debiased estimators using three ingredients: the gradient and Hessian of the loss function and a linear approximation of the target functional. Estimation reduces to solving two risk minimization problems, one for the M-estimand and one for a Riesz representer. The framework accommodates Neyman-orthogonal loss functions that depend on nuisance parameters and extends to vector-valued M-estimands through joint risk minimization. We characterize the efficient influence function and construct efficient autoDML estimators via one-step correction, targeted minimum loss estimation, and sieve-based plug-in methods. Under quadratic risk, these estimators satisfy double robustness for linear functionals. We further show that they are robust to mild misspecification of the M-estimand model, incurring only second-order bias. We illustrate the method by estimating long-term survival probabilities under a semiparametric two-parameter beta-geometric failure model.

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arXiv2026

Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts

We introduce efficient plug-in (EP) learning, a novel framework for the estimation of heterogeneous causal contrasts, such as the conditional average treatment effect and conditional relative risk. The EP-learning framework enjoys the same oracle efficiency as Neyman-orthogonal learning strategies, such as DR-learning and R-learning, while addressing some of their primary drawbacks: (i) their practical applicability can be hindered by non-convex loss functions; and (ii) they may suffer from poor performance and instability due to inverse probability weighting and pseudo-outcomes that violate bounds. To overcome these issues, the EP-learner leverages an efficient plug-in estimator of the population risk function for the causal contrast. In doing so, it inherits the stability of plug-in strategies such as T-learning, while improving on their efficiency. Under reasonable conditions, EP-learners based on empirical risk minimization are oracle-efficient, exhibiting asymptotic equivalence to the minimizer of an oracle-efficient one-step debiased estimator of the population risk function. In simulation experiments, we show that EP-learners of the conditional average treatment effect and conditional relative risk outperform state-of-the-art competitors, including the T-learner, R-learner, and DR-learner. Open-source implementations of the proposed methods are available in our \texttt{R} package \texttt{hte3}.

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arXiv2026

Adaptive debiased machine learning using data-driven model selection techniques

Debiased machine learning estimators for smooth functionals in nonparametric models can exhibit substantial variability and instability, often leading practitioners to instead rely on parametric or semiparametric working models. Such models, however, may be misspecified and can therefore introduce bias. We study how data-driven model selection can be combined with debiased machine learning to construct estimators that adapt to structure in the data-generating distribution. To this end, we propose Adaptive Debiased Machine Learning (ADML), a nonparametric framework for constructing superefficient estimators of pathwise differentiable parameters. The framework unifies a broad class of previously proposed adaptive estimators, including methods based on variable selection, learned feature representations, and collaborative targeted learning. It requires only high-level conditions and approximate validity of the selection procedure, which are implied by lower-level conditions already assumed in important settings, including sieve-based selection, sparsity-based methods such as the Lasso, and data-adaptive feature representations. We show that ADML estimators yield regular and efficient root-$n$ inference for an oracle projection parameter induced by a data-adaptive oracle submodel. This oracle parameter coincides with the target parameter at the true distribution but typically has a smaller efficiency bound, thereby yielding superefficiency for the target parameter. As a practical illustration, we introduce a broad class of automatic ADML estimators for continuous linear functionals of the outcome regression, in which model selection is performed directly on the regression itself. Motivated by overlap challenges in causal inference, we develop new superefficient plug-in estimators for the average treatment effect based on calibration in semiparametric regression models.

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arXiv2026

A Researcher's Guide to Empirical Risk Minimization

This guide provides a reference for high-probability regret bounds in empirical risk minimization (ERM). The presentation is modular: we begin with intuition and general proof strategies, then state broadly applicable guarantees under high-level conditions and provide tools for verifying them for specific losses and function classes. We emphasize that many ERM rate derivations can be organized around a three-step recipe -- a basic inequality, a uniform local concentration bound, and a fixed-point argument -- which yields regret bounds in terms of a critical radius, defined via localized Rademacher complexity, under a mild Bernstein-type variance-risk condition. To make these bounds concrete, we upper bound the critical radius using local maximal inequalities and metric-entropy integrals, thereby recovering familiar rates for VC-subgraph, Sobolev/Hölder, and bounded-variation classes. We also study ERM with nuisance components -- including weighted ERM and Neyman-orthogonal losses -- as they arise in causal inference, missing data, and domain adaptation. Following the orthogonal statistical learning framework, we highlight that these problems often admit regret-transfer bounds linking regret under an estimated loss to population regret under the target loss. These bounds typically decompose the regret into (i) statistical error under the estimated loss and (ii) approximation error due to nuisance estimation. Under sample splitting or cross-fitting, the first term can be controlled using standard fixed-loss ERM regret bounds, while the second depends only on nuisance-estimation accuracy. As a novel contribution, we also treat the in-sample regime, in which the nuisances and the ERM are fit on the same data, deriving regret bounds and showing that fast oracle rates remain attainable under suitable smoothness and Donsker-type conditions.

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arXiv2026

Hybrid Meta-learners for Estimating Heterogeneous Treatment Effects

Estimating conditional average treatment effects (CATE) from observational data involves modeling decisions that differ from supervised learning, particularly concerning how to regularize model complexity. Previous approaches can be grouped into two primary "meta-learner" paradigms that impose distinct inductive biases. Indirect meta-learners first fit and regularize separate potential outcome (PO) models and then estimate CATE by taking their difference, whereas direct meta-learners construct and directly regularize estimators for the CATE function itself. Neither approach consistently outperforms the other across all scenarios: indirect learners perform well when the PO functions are simple, while direct learners outperform when the CATE is simpler than individual PO functions. In this paper, we introduce the Hybrid Learner (H-learner), a novel regularization strategy that interpolates between the direct and indirect regularizations depending on the dataset at hand. The H-learner achieves this by learning intermediate functions whose difference closely approximates the CATE without necessarily requiring accurate individual approximations of the POs themselves. We demonstrate that intentionally allowing suboptimal fits to the POs improves the bias-variance tradeoff in estimating CATE. Experiments conducted on semi-synthetic and real-world benchmark datasets illustrate that the H-learner consistently operates at the Pareto frontier, effectively combining the strengths of both direct and indirect meta-learners.

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arXiv2026

Nonparametric Instrumental Variable Inference with Many Weak Instruments

We study inference on linear functionals in the nonparametric instrumental variable (NPIV) problem with a discretely-valued instrument under a many-weak-instruments asymptotic regime, where the number of instrument values grows with the sample size. A key motivating example is estimating long-term causal effects in a new experiment with only short-term outcomes, using past experiments to instrument for the effect of short- on long-term outcomes. Here, the assignment to a past experiment serves as the instrument: we have many past experiments but only a limited number of units in each. Since the structural function is nonparametric but constrained by only finitely many moment restrictions, point identification typically fails. To address this, we consider linear functionals of the minimum-norm solution to the moment restrictions, which is always well-defined. As the number of instrument levels grows, these functionals define an approximating sequence to a target functional, replacing point identification with a weaker asymptotic notion suited to discrete instruments. Extending the Jackknife Instrumental Variable Estimator (JIVE) beyond the classical parametric setting, we propose npJIVE, a nonparametric estimator for solutions to linear inverse problems with many weak instruments. We construct automatic debiased machine learning estimators for linear functionals of both the structural function and its minimum-norm projection, and establish their efficiency in the many-weak-instruments regime. To do so, we develop a general semiparametric efficiency theory for regular estimators under weak identification and many-weak-instrument asymptotics.

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