Sparse Additive Off-Policy Evaluation for Reinforcement Learning with Potentially Limited Number of Trajectories

We develop a new framework for flexible, nonlinear, and interpretable off-policy evaluation for infinite-horizon reinforcement learning. To handle large state spaces and support transparent decision-making, we model the Q-function using a nonlinear function class with a sparse additive structure. We derive high-probability finite-sample error bounds for estimating the value function of a target policy and show that the bounds depend only logarithmically on the ambient dimension $d$, thereby alleviating the curse of dimensionality. In contrast to most existing theory for off-policy evaluation, which typically assumes access to many trajectories, our analysis guarantees accurate value estimation when either the number of trajectories or the time horizon is sufficiently large. In addition, we propose a group-sparsity-based feature screening procedure that identifies, with high probability, a reduced feature set containing all relevant covariates. Numerical experiments demonstrate the effectiveness of the proposed approach.

When Offline Evaluation Misleads: A Diagnostic Protocol for Reward and Policy Selection in Delayed-Feedback Contextual Bandits

Personalizing marketing messages with contextual multi-armed bandits (CMABs) drives real business value, yet the objective that ultimately matters - a downstream conversion - is observed only weeks later, too late to drive online learning. Teams therefore train the bandit on a fast proxy reward, and separately must judge whether a contextual bandit is worth its complexity over sending one best message. Settling both decisions with the usual offline checks - a batch off-policy estimate, a marginal arm-discrimination test, a confidence interval - can mislead systematically under delayed feedback. We give an ordered diagnostic protocol that screens a reward-and-policy candidate on two axes, alignment (does optimizing the reward move the north-star?) and learnability (can the bandit identify the reward-optimal policy?), before trusting any reported lift. We validate it where the truth is known - a public off-policy-evaluation benchmark and a controllable synthetic generator - and illustrate it on a deployed large-marketplace push system (where, with five arms and one split, the evidence is directional rather than powered). Two lessons recur. (N1) A single offline number can mis-rank rewards: a denser reward signal gives the bandit more to learn from, so rewards that look tied in a static estimate pull apart once learning happens online. (N2) If you cannot tell in advance which single message is best, a per-user policy partly just avoids betting on the wrong one - that looks like personalization but is really robustness, so a "personalization premium" is easily overstated. Our contribution is methodological rather than algorithmic: the ordered protocol, the two lessons it surfaces, and the end-to-end experience of applying it to a delayed-feedback CMAB.

Learning from the Unseen: Offline Reinforcement Learning with Hidden Actions

Standard offline reinforcement learning (RL) algorithms typically assume that the actions in the dataset are observed without error. However, in many real-world applications, the true actions are unobserved and only noisy proxies are available, causing existing RL methods to yield biased and potentially misleading conclusions. We study off-policy evaluation in infinite-horizon discounted Markov decision processes with hidden actions. By leveraging the next-state variable as a natural proxy for the unobserved action, we establish identification of the policy value and propose an influence-function-based estimator called LURE (Learning from the Unseen: Robust Estimator). LURE is multiply robust, remaining consistent under several combinations of correctly specified nuisance components, and is asymptotically normal, enabling valid statistical inference. To our knowledge, this is the first work to address offline RL with hidden actions. We demonstrate LURE's effectiveness through simulations and a sepsis management application using the MIMIC-III database.

Cross-Domain Off-Policy Evaluation and Learning for Contextual Bandits

Off-Policy Evaluation and Learning (OPE/L) in contextual bandits is rapidly gaining popularity in real systems because new policies can be evaluated and learned securely using only historical logged data. However, existing methods in OPE/L cannot handle many challenging but prevalent scenarios such as few-shot data, deterministic logging policies, and new actions. In many applications, such as personalized medicine, content recommendations, education, and advertising, we need to evaluate and learn new policies in the presence of these challenges. Existing methods cannot evaluate and optimize effectively in these situations due to the notorious variance issue or limited exploration in the logged data. To enable OPE/L even under these unsolved challenges, we propose a new problem setup of Cross-Domain OPE/L, where we have access not only to the logged data from the target domain in which the new policy will be implemented but also to logged datasets collected from other domains. This novel formulation is widely applicable because we can often use historical data not only from the target hospital, country, device, or user segment but also from other hospitals, countries, devices, or segments. We develop a new estimator and policy gradient method to solve OPE/L by leveraging both target and source datasets, resulting in substantially enhanced OPE/L in the previously unsolved situations in our empirical evaluations.

Kernel weighted importance sampling for off-policy evaluation in contextual bandits

This article presents a novel estimator for performing off-policy evaluation using only offline data for contextual bandits. The proposed estimator, Kernel-WIS is demonstrated to be asymptotically consistent and to empirically outperform strong baselines (including vanilla weighted importance sampling), particularly under complex conditions including behaviour policy miss-specification. The benefit of Kernel-WIS is derived from combining the bounded property of vanilla weighted importance sampling with the linearity of vanilla importance sampling.

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 log-ratio approximation error and a statistical error governed by the complexity of the ratio hypothesis class. 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.

Off-Policy Evaluation for Missingness-Aware Policies in MDPs with Rewards Missing Not at Random

In offline Reinforcement Learning, immediate rewards in logged batch data are often unobserved due to sparse or irregular record-keeping, or censored beyond certain reward values. This issue arises in practical settings, including health care and marketing. We investigate off-policy evaluation (OPE) in finite-horizon Markov decision processes when rewards are missing not at random (MNAR), which breaks ignorability and induces selection bias even after conditioning on states and actions. To address this, we formalize a reward-dependent propensity model and use future states as shadow variables to identify the full-data conditional mean reward. We further introduce a bridge function that recovers the conditional mean reward without explicitly modeling the MNAR mechanism, and estimate it via a min-max procedure to avoid double sampling. Building upon these identification results, we propose an Fitted-Q-Evaluation-style estimator that propagates the recovered rewards while allowing target policies to depend on past missingness indicators. Finally, we establish consistency and finite-sample error bounds for our OPE estimator, and show through experiments the strong performance of our method compared to existing methods on simulated and MIMIC-III Sepsis data.