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Machine learning is increasingly used to support decision-making in high-stakes domains such as precision medicine. Unlike traditional predictive models, decision-making models must take into account the effects of future actions that may not be directly observed in the available data. This mismatch between training data and target distribution introduces challenges. In such cases, data may be biased, confounded, or lacking sufficient support to evaluate alternative actions, and standard statistical learning methods can be misleading. This thesis addresses the problem of evaluating and learning decision policies under the above challenges. A central goal is to enable valid predictions about the consequences of implementing new policies, even when the data are incomplete or collected under conditions different from those under which the policy will be applied. We develop methods that explicitly model uncertainty and bias, allowing for valid performance guarantees in these scenarios.

In the first research paper, we focus on multi-objective decision support by learning Pareto-efficient decisions and provide finite-sample guarantees. In the following two research papers, we address policy evaluation: first in the case of observational data, and then in the case of a randomized trial. We propose robust reweighting techniques to evaluate the distributional performance of a given policy. For observational data, where the past policy is unknown, we provide valid performance guarantees under confounding. For randomized controlled trials, we instead provide valid performance guarantees when generalizing the trial results to broader populations. The fourth research paper addresses trade-offs between minimizing treatment risk while reducing harm. We propose a learning method that controls harm in a partially identified setting. In the final research paper, we study decision-making with missing data. Instead of imputing missing values, we propose a method that can handle missingness directly in the policy learning to improve upon a baseline policy.

The thesis is focused on methods that are certified to be statistically valid under credible assumptions. The aim is to make data-driven decision-making in sensitive applications safer and more trustworthy.

We consider the problem of evaluating the performance of a decision policy using past observational data. The outcome of a policy is measured in terms of a loss (aka. disutility or negative reward) and the main problem is making valid inferences about its out-of-sample loss when the past data was observed under a different and possibly unknown policy. Using a sample-splitting method, we show that it is possible to draw such inferences with finite-sample coverage guarantees about the entire loss distribution, rather than just its mean. Importantly, the method takes into account model misspecifications of the past policy - including unmeasured confounding. The evaluation method can be used to certify the performance of a policy using observational data under a specified range of credible model assumptions.

The paper considers the problem of multi-objective decision support when outcomes are uncertain. We extend the concept of Pareto-efficient decisions to take into account the uncertainty of decision outcomes across varying contexts. This enables quantifying trade-offs between decisions in terms of tail outcomes that are relevant in safety-critical applications. We propose a method for learning efficient decisions with statistical confidence, building on results from the conformal prediction literature. The method adapts to weak or nonexistent context covariate overlap and its statistical guarantees are evaluated using both synthetic and real data.