This paper studies how to integrate historical control data with experimental data to enhance A/B testing, while addressing the distributional shift between historical and experimental datasets. We propose a pessimistic data integration method that combines two causal effect estimators constructed based on experimental and historical datasets. Our main idea is to conceptualize the weight function for this combination as a policy so that existing pessimistic policy learning algorithms are applicable to learn the optimal weight that minimizes the resulting weighted estimator's mean squared error. Additionally, we conduct comprehensive theoretical and empirical analyses to compare our method against various baseline estimators across five scenarios. Both our theoretical and numerical findings demonstrate that the proposed estimator achieves near-optimal performance across all scenarios.

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.

We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs) with unobserved confounding. Recent advances have introduced bridge-function to circumvent unmeasured confounding and develop estimators for the policy value, yet the statistical error bounds of them related to the length of horizon T and the size of the state-action space |O||A| remain largely unexplored. In this paper, we systematically investigate the finite-sample error bounds of OPE estimators in finite-horizon tabular confounded POMDPs. Specifically, we show that under certain rank conditions, the estimation error for policy value can achieve a rate of O(T1.5/ n), excluding the cardinality of the observation space |O| and the action space |A|. With an additional mild condition on the concentrability coefficients in confounded POMDPs, the rate of estimation error can be improved to O(T/ n).

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.

While RLHF has demonstrated promising results, many algorithms are highly sensitive to misspecifications in the underlying preference model (e.g., the Bradley-Terry model), the reference policy, or the reward function, resulting in undesirable fine-tuning. To address model misspecification, we propose a doubly robust preference optimization algorithm that remains consistent when either the preference model or the reference policy is correctly specified (without requiring both). Our proposal demonstrates superior and more robust performance than state-of-the-art algorithms, both in theory and in practice.

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.

Two-stage recommender systems first choose a candidate generator and then rank items within the generated set. Because the generator decides which items are available to the ranker, changing the generator changes both the policy value and the data support used to estimate that value. This creates an offline selection problem that standard single-stage objectives do not capture: a policy may look good under a retrieval score or a raw off-policy value estimate, but still be unreliable if it depends on weakly supported generator-item pairs. We propose CASP (Coupled Action-Set Pessimism), a support-aware offline selector for finite libraries of two-stage recommender policies. CASP combines doubly robust value estimation with a support-burden penalty. We show that stagewise rules that ignore downstream continuation value can be arbitrarily suboptimal, and we derive population, finite-class, and reconstructed-propensity guarantees for conservative selection. In simulations and a reconstructed MovieLens 1M application, CASP selects lower-burden policies when estimated value and support credibility are in tension.