Calibrated Probabilistic Forecasts for Arbitrary Sequences

Real-world data streams can change unpredictably due to distribution shifts, feedback loops and adversarial actors, which challenges the validity of forecasts. We present a forecasting framework ensuring valid uncertainty estimates regardless of how data evolves. Leveraging the concept of Blackwell approachability from game theory, we introduce a forecasting framework that guarantees calibrated uncertainties for outcomes in any compact space (e.g., classification or bounded regression). We extend this framework to recalibrate existing forecasters, guaranteeing calibration without sacrificing predictive performance. We implement both general-purpose gradient-based algorithms and algorithms optimized for popular special cases of our framework. Empirically, our algorithms improve calibration and downstream decision-making for energy systems.