Learning Decision-Focused Uncertainty Representations: Theory and Applications in Sustainability

Managing risks arising from decision-making under uncertainty is a paramount challenge in many sustainability and energy applications. The threat of climate change paired with the increasing complexity of energy systems has made it more important than ever to develop artificial intelligence (AI) and machine learning (ML) methods that can address these challenges. However, standard AI and ML methods suffer from a trade-off between accuracy and reliability. While modern AI models are increasingly capable and accurate, they generally lack rigorous uncertainty quantification for reliability guarantees. On the other hand, traditional methods for uncertainty quantification often rely on strong assumptions and are not designed to optimize decision quality. As a result, existing methods for learning uncertainty representations are often not well-suited for real-world decision-making applications. This thesis develops new methods for overcoming this trade-off by learning uncertainty representations that are directly useful for decision-making. The first part of the thesis studies batch decision problems, where a model is trained on historical data and then used to make one-shot decisions. A central theme is that good predictions alone are not enough: the uncertainty must be shaped to match the downstream task. Instead, we develop a general framework for decision-focused learning of uncertainty representations, which can be tailored to a wide range of optimization problems and risk guarantees. By leveraging differentiable optimization, we develop end-to-end methods for learning calibrated confidence scores for achieving tail-risk guarantees, uncertainty sets for robust optimization, and generative models for Wasserstein distributionally robust optimization. We also extend decision-focused learning to diffusion models so that full predictive distributions can be used for stochastic optimization. Across energy storage, generator scheduling, and related applications, these methods improve robustness and decision quality while retaining theoretical guarantees or tractable optimization. The second part of the thesis turns to sequential decision-making. For voltage regulation in distribution grids with uncertain topology, the thesis develops an online control algorithm with a finite-mistake guarantee, showing that safe control can be achieved even while the system is still being learned. The thesis also introduces SustainGym, a benchmark suite of reinforcement learning environments for sustainability applications, including electric vehicle charging, electricity markets, datacenters, cogeneration, and building control. SustainGym exposes realistic distribution shifts, physical constraints, and multi-agent interactions that are often absent from standard benchmarks, and it reveals how brittle off-the-shelf reinforcement learning (RL) methods can be in these settings. We develop a new family of distributionally robust RL algorithms that can learn policies with strong out-of-distribution generalization guarantees, and we show that these methods can achieve superior performance in SustainGym and game-playing environments. Taken together, the thesis argues for a general principle: uncertainty should be learned, calibrated, and evaluated in terms of the decisions it enables. By connecting uncertainty quantification, optimization, online learning, and reinforcement learning, this work provides both theory and practical tools for building reliable decision systems in sustainability-critical applications.