Quantifying the uncertainty of machine learning models is crucial for numerous applications, particularly in large-scale real-world scenarios where prediction sets, rather than point predictions, enable more flexible and informed decision making. Uncertainty quantification (UQ) methods are essential for characterizing the unpredictibility arising in various real-world problems across science and engineering. Initially proposed by Vovk et al. [2005], CP is a popular distribution-free method for UQ, largely due to its ability to provide finite-sample coverage guarantees and its computational efficiency. Most studies in CP focus on constructing prediction intervals based on a fitted mean model. This work introduces a novel setting where the value of interest is estimated using only a pair of valid upper and lower bounds, instead of a mean model. While valid bounds themselves provide perfect coverage by definition, they can sometimes be overly conservative. By slightly reducing the coverage level, these bounds can be tightened, resulting in significantly smaller intervals with theoretical guarantees and greater utility for decision making.

This paper introduces Dual Interior Point Learning (DIPL) and Dual Supergradient Learning (DSL) to learn dual feasible solutions to parametric linear programs with bounded variables, which are pervasive across many industries. DIPL mimics a novel dual interior point algorithm while DSL mimics classical dual supergradient ascent. DIPL and DSL ensure dual feasibility by predicting dual variables associated with the constraints then exploiting the flexibility of the duals of the bound constraints. DIPL and DSL complement existing primal learning methods by providing a certificate of quality. They are shown to produce high-fidelity dual-feasible solutions to large-scale optimal power flow problems providing valid dual bounds under 0.5% optimality gap.

This paper considers optimization proxies for Optimal Power Flow (OPF), i.e., machine-learning models that approximate the input/output relationship of OPF. Recent work has focused on showing that such proxies can be of high fidelity. However, their training requires significant data, each instance necessitating the (offline) solving of an OPF for a sample of the input distribution. To meet the requirements of market-clearing applications, this paper proposes Bucketized Active Sampling (BAS), a novel active learning framework that aims at training the best possible OPF proxy within a time limit. BAS partitions the input distribution into buckets and uses an acquisition function to determine where to sample next. By applying the same partitioning to the validation set, BAS leverages labeled validation samples in the selection of unlabeled samples. BAS also relies on an adaptive learning rate that increases and decreases over time. Experimental results demonstrate the benefits of BAS.