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1. Balanced Policy Evaluation and Learning

   Kallus, Nathan (January 2018, Advances in neural information processing systems)

   We present a new approach to the problems of evaluating and learning personalized decision policies from observational data of past contexts, decisions, and outcomes. Only the outcome of the enacted decision is available and the historical policy is unknown. These problems arise in personalized medicine using electronic health records and in internet advertising. Existing approaches use inverse propensity weighting (or, doubly robust versions) to make historical outcome (or, residual) data look like it were generated by a new policy being evaluated or learned. But this relies on a plug-in approach that rejects data points with a decision that disagrees with the new policy, leading to high variance estimates and ineffective learning. We propose a new, balance-based approach that too makes the data look like the new policy but does so directly by finding weights that optimize for balance between the weighted data and the target policy in the given, finite sample, which is equivalent to minimizing worst-case or posterior conditional mean square error. Our policy learner proceeds as a two-level optimization problem over policies and weights. We demonstrate that this approach markedly outperforms existing ones both in evaluation and learning, which is unsurprising given the wider support of balance-based weights. We establish extensive theoretical consistency guarantees and regret bounds that support this empirical success. 

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2. Stateful Offline Contextual Policy Evaluation and Learning

   Nathan Kallus, Angela Zhou (January 2022, Proceedings of The 25th International Conference on Artificial Intelligence and Statistics)

   We study off-policy evaluation and learning from sequential data in a structured class of Markov decision processes that arise from repeated interactions with an exogenous sequence of arrivals with contexts, which generate unknown individual-level responses to agent actions. This model can be thought of as an offline generalization of contextual bandits with resource constraints. We formalize the relevant causal structure of problems such as dynamic personalized pricing and other operations management problems in the presence of potentially high-dimensional user types. The key insight is that an individual-level response is often not causally affected by the state variable and can therefore easily be generalized across timesteps and states. When this is true, we study implications for (doubly robust) off-policy evaluation and learning by instead leveraging single time-step evaluation, estimating the expectation over a single arrival via data from a population, for fitted-value iteration in a marginal MDP. We study sample complexity and analyze error amplification that leads to the persistence, rather than attenuation, of confounding error over time. In simulations of dynamic and capacitated pricing, we show improved out-of-sample policy performance in this class of relevant problems. 

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3. Data-driven Competitive Algorithms for Online Knapsack and Set Cover

   Zeynali, Ali; Sun, Bo; Hajiesmaili, Mohammad; Wierman, Adam (February 2021, Proceedings of the AAAI Conference on Artificial Intelligence)

   null (Ed.)

   The design of online algorithms has tended to focus on algorithms with worst-case guarantees, e.g., bounds on the competitive ratio. However, it is well-known that such algorithms are often overly pessimistic, performing sub-optimally on non-worst-case inputs. In this paper, we develop an approach for data-driven design of online algorithms that maintain near-optimal worst-case guarantees while also performing learning in order to perform well for typical inputs. Our approach is to identify policy classes that admit global worst-case guarantees, and then perform learning using historical data within the policy classes. We demonstrate the approach in the context of two classical problems, online knapsack, and online set cover, proving competitive bounds for rich policy classes in each case. Additionally, we illustrate the practical implications via a case study on electric vehicle charging. 

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4. 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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5. 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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