Risk-Sensitive Statistical Learning: Methods, Algorithms, and Theories

The research in this project will address a fundamental challenge in a variety of critical fields such as medicine, finance, and robotics: making decisions that not only aim for the best average outcomes but also minimize risks to individuals. For instance, when selecting a medical treatment, it is not enough to know that a treatment works well on average; we need to ensure that it benefits a large proportion of patients, say 95%, without causing harm. Current statistical learning methods, however, often overlook such nuanced considerations of risk, leading to a significant disconnect between theoretical advancements and practical needs. This proposal seeks to close this gap by developing a new framework for risk-sensitive decision-making. By incorporating risk assessments into the decision-making process, our research aims to advance scientific knowledge and contribute to the general interest by improving healthcare outcomes, financial stability, and the safety and effectiveness of robotic systems. The project will also support education and promote diversity by providing training opportunities for students at various levels and developing user-friendly, open-source software to make these advanced methods accessible to practitioners. The research will focus on the development of innovative methods for risk-sensitive statistical learning, aiming to improve decision-making processes in areas where outcomes' variability can significantly impact overall success. The project is structured around four specific aims. The first aim is to develop quantile-constrained statistical learning. A particular example is to optimize average outcomes under constraints that ensure a minimum benefit level across a defined proportion of a population. This involves formulating the problem as a constrained optimization issue with stochastic boundaries, proposing novel algorithms, and deriving asymptotic results for estimator analysis. The second aim is to develop methods for risk-sensitive deep reinforcement learning. This is to create theoretically grounded algorithms that utilize deep neural networks to derive optimal decision rules, incorporating variance and other risk considerations to ensure decisions are robust under uncertainty. The third aim is to address risk-sensitive bandit problems through the development of both frequentist and Bayesian models and algorithms, aiming to achieve optimal regrets while considering risk. The final aim is to extend the methods and results to encompass the broad class of coherent risk measures, thereby enhancing the applicability and impact of the research across various domains. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.