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1. CAB: Continuous Adaptive Blending Estimator for Policy Evaluation and Learning

   Su, Yi; Wang, Lequn; Santacatterina, Michele; Joachims, Thorsten (April 2019, Proceedings of Machine Learning Research)

   The ability to perform offline A/B-testing and off-policy learning using logged contextual bandit feedback is highly desirable in a broad range of applications, including recommender systems, search engines, ad placement, and personalized health care. Both offline A/B-testing and offpolicy learning require a counterfactual estimator that evaluates how some new policy would have performed, if it had been used instead of the logging policy. In this paper, we present and analyze a family of counterfactual estimators which subsumes most estimators proposed to date. Most importantly, this analysis identifies a new estimator – called Continuous Adaptive Blending (CAB) – which enjoys many advantageous theoretical and practical properties. In particular, it can be substantially less biased than clipped Inverse Propensity Score (IPS) weighting and the Direct Method, and it can have less variance than Doubly Robust and IPS estimators. In addition, it is subdifferentiable such that it can be used for learning, unlike the SWITCH estimator. Experimental results show that CAB provides excellent evaluation accuracy and outperforms other counterfactual estimators in terms of learning performance. 

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2. Policy Evaluation and Optimization with Continuous Treatments

   Kallus, Nathan; Zhou, Angela (January 2018, Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS))

   We study the problem of policy evaluation and learning from batched contextual bandit data when treatments are continuous, going beyond previous work on discrete treatments. Previous work for discrete treatment/action spaces focuses on inverse probability weighting (IPW) and doubly robust (DR) methods that use a rejection sampling approach for evaluation and the equivalent weighted classification problem for learning. In the continuous setting, this reduction fails as we would almost surely reject all observations. To tackle the case of continuous treatments, we extend the IPW and DR approaches to the continuous setting using a kernel function that leverages treatment proximity to attenuate discrete rejection. Our policy estimator is consistent and we characterize the optimal bandwidth. The resulting continuous policy optimizer (CPO) approach using our estimator achieves convergent regret and approaches the best-in-class policy for learnable policy classes. We demonstrate that the estimator performs well and, in particular, outperforms a discretization-based benchmark. We further study the performance of our policy optimizer in a case study on personalized dosing based on a dataset of Warfarin patients, their covariates, and final therapeutic doses. Our learned policy outperforms benchmarks and nears the oracle-best linear policy. 

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3. POTEC: Off-Policy Contextual Bandits for Large Action Spaces via Policy Decomposition

   Saito, Yuta; Yao, Yihan; Joachims, Thorsten (June 2025, International Conference on Representation Learning (ICLR))

   We study off-policy learning (OPL) of contextual bandit policies in large discrete action spaces where existing methods – most of which rely crucially on reward-regression models or importance-weighted policy gradients – fail due to excessive bias or variance. To overcome these issues in OPL, we propose a novel two-stage algorithm, called Policy Optimization via Two-Stage Policy Decomposition (POTEC). It leverages clustering in the action space and learns two different policies via policy- and regression-based approaches, respectively. In particular, we derive a novel low-variance gradient estimator that enables to learn a first-stage policy for cluster selection efficiently via a policy-based approach. To select a specific action within the cluster sampled by the first-stage policy, POTEC uses a second-stage policy derived from a regression-based approach within each cluster. We show that a local correctness condition, which only requires that the regression model preserves the relative expected reward differences of the actions within each cluster, ensures that our policy-gradient estimator is unbiased and the second-stage policy is optimal. We also show that POTEC provides a strict generalization of policyand regression-based approaches and their associated assumptions. Comprehensive experiments demonstrate that POTEC provides substantial improvements in OPL effectiveness particularly in large and structured action spaces. 

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4. An Off-Policy Learning Approach for Steering Sentence Generation towards Personalization

   https://doi.org/10.1145/3705328.3748088  

   Kiyohara, Haruka; Cao, Daniel Yiming; Saito, Yuta; Joachims, Thorsten (September 2025, ACM)

   We study the problem of personalizing the output of a large language model (LLM) by training on logged bandit feedback (e.g., personalizing movie descriptions based on likes). While one may naively treat this as a standard off-policy contextual bandit problem, the large action space and the large parameter space make naive applications of off-policy learning (OPL) infeasible. We overcome this challenge by learning a prompt policy for a frozen LLM that has only a modest number of parameters. The proposed Direct Sentence Off-policy gradient (DSO) effectively propagates the gradient to the prompt policy space by leveraging the smoothness and overlap in the sentence space. Consequently, DSO substantially reduces variance while also suppressing bias. Empirical results on our newly established suite of benchmarks, called OfflinePrompts, demonstrate the effectiveness of the proposed approach in generating personalized descriptions for movie recommendations, particularly when the number of candidate prompts and reward noise are large. 

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5. Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning

   Bibaut, Aurelien; Kallus, Nathan; Dimakopoulou, Maria; Chambaz, Antoine; van der Laan, Mark (January 2021, Advances in neural information processing systems)

   Empirical risk minimization (ERM) is the workhorse of machine learning, whether for classification and regression or for off-policy policy learning, but its model-agnostic guarantees can fail when we use adaptively collected data, such as the result of running a contextual bandit algorithm. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class and provide first-of-their-kind generalization guarantees and fast convergence rates. Our results are based on a new maximal inequality that carefully leverages the importance sampling structure to obtain rates with the good dependence on the exploration rate in the data. For regression, we provide fast rates that leverage the strong convexity of squared-error loss. For policy learning, we provide regret guarantees that close an open gap in the existing literature whenever exploration decays to zero, as is the case for bandit-collected data. An empirical investigation validates our theory. 

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