CAREER: Dynamic Decision-Making Under Uncertainty via Distributionally Robust Optimization

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A wide spectrum of decision problems arising in process control, energy systems operation, supply chain management, investment planning, project management, engineering, economics, etc., involve uncertain parameters whose values are unknown to the decision maker when the decisions are made. Ignoring this uncertainty typically leads to inferior solutions that perform poorly in practice due to the notorious flaw of averages, whereby plans based on the assumption that average conditions pre-vail are usually wrong. These decision problems are often also dynamic in nature they span across multiple time stages and involve high dimensional non-anticipative recourse decisions which further increase the problem complexity. Thus, effective and efficient solution schemes for these decision problems are highly desirable. Traditional solution schemes, however, suffer from the curse of dimensionality and are extremely challenging to solve. Recent advances in distributionally robust optimization (DRO) have been successful in mitigating the intractability of various single-stage decision problems under uncertainty. In DRO, we seek a decision that performs best in view of the most adverse distribution of uncertain parameters that is consistent with the available statistical and structural information. Thus, DRO not only improves computational tractability but also alleviates the overfitting effects characteristic of the traditional solution schemes. By leveraging and inventing new techniques in DRO, the proposed research work aims to significantly advance the state-of-the-art methodologies for addressing the challenges of dynamic decision problems and to initiate the effort for industrial-size applications. The research outputs of this work will have a significant and immediate practical impact on important applications in energy, engineering, machine learning, operations management, finance, etc., and on learning problems in robotics and automatic control. This CAREER work will also advance the state of pedagogy by developing an integrated curriculum that bridges the gap between the deep theory of decision-making under uncertainty and the real-life practice. The proposed curriculum is aimed at future practitioners and researchers, and is designed to equip these experts with the analytical skills and tools to deal with real-life decision-making problems under uncertainty.The proposed research work is aimed at addressing a major gap in the theory and practice of decision-making under uncertainty. It concentrates on four main research thrusts: 1) Derive exact mixed-integer conic programming (MICP) reformulations for convex dynamic problems as well as for dynamic problems with discrete decisions 2) Deal with the case of endogenous uncertainty whose representation depends explicitly on the chosen decisions 3) Systematically integrate data into the description of uncertainty. Obtain provable out-of-sample performance guarantees from the resulting data-driven DRO models 4) Derive exact MICP reformulations for inverse optimization problems in the dynamic setting. The proposed research effort endeavors to develop more powerful solution schemes which leverage standard off-the-shelf MICP solvers for various intractable decision-making problems under uncertainty. The work will establish a new connection between generic dynamic DRO models and renowned classes of mixed-integer conic programs. The resulting connection will give us a better understanding of the inherent difficulty of the decision problems and enable us to derive attractive performance guarantees for the new solution schemes.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.