This work presents the first theoretically justified simultaneous inference framework for off-policy evaluation (OPE). In contrast to existing methods that focus on point estimates or pointwise confidence intervals (CIs), the new framework quantifies global uncertainty across an infinite or continuous initial state space, offering valid inference over the entire state space.

Holdout validation and hyperparameter tuning from data is a long-standing problem in offline reinforcement learning (RL). A standard framework is to use off-policy evaluation (OPE) methods to evaluate and select between different policies, but OPE methods either incur exponential variance (e.g., importance sampling) or have hyperparameters of their own (e.g., FQE and model-based). We focus on model selection for OPE itself, which is even more under-investigated. Concretely, we select among candidate value functions ("model-free") or dynamics models ("model-based") to best assess the performance of a target policy. We develop: (1) new model-free and model-based selectors with theoretical guarantees, and (2) a new experimental protocol for empirically evaluating them. Compared to the model-free protocol in prior works, our new protocol allows for more stable generation and better control of candidate value functions in an optimizationfree manner, and evaluation of model-free and model-based methods alike. We exemplify the protocol on Gym-Hopper, and find that our new model-free selector, LSTD-Tournament, demonstrates promising empirical performance.

Off-policy evaluation (OPE) estimates the performance of a target policy using offline data collected from a behavior policy, and is crucial in domains such as robotics or healthcare where direct interaction with the environment is costly or unsafe. Existing OPE methods are ineffective for high-dimensional, long-horizon problems, due to exponential blow-ups in variance from importance weighting or compounding errors from learned dynamics models. To address these challenges, we propose STITCH-OPE, a model-based generative framework that leverages denoising diffusion for long-horizon OPE in high-dimensional state and action spaces. Starting with a diffusion model pre-trained on the behavior data, STITCHOPE generates synthetic trajectories from the target policy by guiding the denoising process using the score function of the target policy. STITCH-OPE proposes two technical innovations that make it advantageous for OPE: (1) prevents overregularization by subtracting the score of the behavior policy during guidance, and (2) generates long-horizon trajectories by stitching partial trajectories together end-to-end. We provide a theoretical guarantee that under mild assumptions, these modifications result in an exponential reduction in variance versus long-horizon trajectory diffusion.

Off-policy evaluation (OPE) estimates the performance of a target policy using offline data collected from a behavior policy, and is crucial in domains such as robotics or healthcare where direct interaction with the environment is costly or unsafe. Existing OPE methods are ineffective for high-dimensional, long-horizon problems, due to exponential blow-ups in variance from importance weighting or compounding errors from learned dynamics models. To address these challenges, we propose STITCH-OPE, a model-based generative framework that leverages denoising diffusion for long-horizon OPE in high-dimensional state and action spaces. Starting with a diffusion model pre-trained on the behavior data, STITCH-OPE generates synthetic trajectories from the target policy by guiding the denoising process using the score function of the target policy. STITCH-OPE proposes two technical innovations that make it advantageous for OPE: (1) prevents over-regularization by subtracting the score of the behavior policy during guidance, and (2) generates long-horizon trajectories by stitching partial trajectories together end-to-end. We provide a theoretical guarantee that under mild assumptions, these modifications result in an exponential reduction in variance versus long-horizon trajectory diffusion. Experiments on the D4RL and OpenAI Gym benchmarks show substantial improvement in mean squared error, correlation, and regret metrics compared to state-of-the-art OPE methods.

Off-policy evaluation (OPE) estimates the value of a target treatment policy (e.g., a recommender system) using data collected by a different logging policy. It enables high-stakes experimentation without live deployment, yet in practice accuracy depends heavily on the logging policy used to collect data for computing the estimate. We study how to design logging policies that minimize OPE error for given target policies. We characterize a fundamental reward-coverage tradeoff: concentrating probability mass on high-reward actions reduces variance but risks missing signal on actions the target policy may take. We propose a unifying framework for logging policy design and derive optimal policies in canonical informational regimes where the target policy and reward distribution are (i) known, (ii) unknown, and (iii) partially known through priors or noisy estimates at logging time. Our results provide actionable guidance for firms choosing among multiple candidate recommendation systems. We demonstrate the importance of treatment selection when gathering data for OPE, and describe theoretically optimal approaches when this is a firm's primary objective. We also distill practical design principles for selecting logging policies when operational constraints prevent implementing the theoretical optimum.

Off-policy evaluation (OPE) is important for closing the gap between offline training and evaluation of reinforcement learning (RL), by estimating performance and/or rank of target (evaluation) policies using offline trajectories only. It can improve the safety and efficiency of data collection and policy testing procedures in situations where online deployments are expensive, such as healthcare. However, existing OPE methods fall short in estimating human feedback (HF) signals, as HF may be conditioned over multiple underlying factors and is only sparsely available; as opposed to the agent-defined environmental rewards (used in policy optimization), which are usually determined over parametric functions or distributions. Consequently, the nature of HF signals makes extrapolating accurate OPE estimations to be challenging. To resolve this, we introduce an OPE for HF (OPEHF) framework that revives existing OPE methods in order to accurately evaluate the HF signals. Specifically, we develop an immediate human reward (IHR) reconstruction approach, regularized by environmental knowledge distilled in a latent space that captures the underlying dynamics of state transitions as well as issuing HF signals. Our approach has been tested over two real-world experiments, adaptive in-vivo neurostimulation and intelligent tutoring, as well as in a simulation environment (visual Q&A). Results show that our approach significantly improves the performance toward estimating HF signals accurately, compared to directly applying (variants of) existing OPE methods.

In this Appendix we provide additional details about the MSLR-WEB30K data and the experimental protocol that we followed, we prove Lemma 11 of the main paper, and we show additional results on the MSLR-WEB30K and the simulated data.

We study the problem of off-policy evaluation from batched contextual bandit data with multidimensional actions, often termed slates. The problem is common to recommender systems and user-interface optimization, and it is particularly challenging because of the combinatorially-sized action space. Swaminathan et al. (2017) have proposed the pseudoinverse (PI) estimator under the assumption that the conditional mean rewards are additive in actions. Using control variates, we consider a large class of unbiased estimators that includes as specific cases the PI estimator and (asymptotically) its self-normalized variant. By optimizing over this class, we obtain new estimators with risk improvement guarantees over both the PI and the self-normalized PI estimators.