The use of residential photovoltaics has increased dramatically in recent years. With battery systems becoming more affordable, the optimal operation of a photovoltaic-battery system can bring significant savings to households. Optimal control requires correct forecasts of underlying parameters, such as photovoltaic power generation, to schedule the battery. While forecasting models have become increasingly accurate due to algorithmic advances and data availability, accuracy is typically measured in generic metrics which might not align with the downstream application. This study proposes a decision-focused learning framework that integrates optimization and prediction by training a Long Short-Term Memory photovoltaic energy forecaster on the downstream optimal scheduling of a battery system. The proposed methodology is compared against a standard two-phase approach. Across a 14-month evaluation period, the decision-focused method reduced average electricity costs across twenty buildings by 3.6% when normalized against performance bounds defined by a perfect forecast and a baseline of no optimization. Critically, this financial improvement was achieved despite the model exhibiting a root mean squared error of 19.9%, significantly higher than the decoupled model's 8.2%. Warm-starting the decision-focused model further improves results, lowering average cost by approximately 8%, while also mitigating the negative impact on statistical accuracy (root mean squared error of 13.7%). The findings are statistically significant at the 0.001 level across the twenty households and for each household individually. These results demonstrate that aligning forecast models with optimization goals is key for achieving cost advantages in PV-battery systems. Future research should replicate these findings on other datasets, alternate forecasting models and alternate optimization algorithms.

The classic concept of "calibrated forecasts" and its more recent refinement, "calibeating," are defined with respect to the standard quadratic scoring rule. We extend these notions to the class of $\textit{proper}$ scoring rules (for which the best forecast is the true distribution) and define $\textit{proper-calibration}$ and $\textit{proper-calibeating}$ by requiring the errors to converge to zero uniformly over all bounded proper scoring rules. We first establish that calibration always implies proper-calibration, whereas calibeating need not imply proper-calibeating. Second, we show how to guarantee proper-calibeating and proper-multicalibeating. Finally, we demonstrate the equivalence between proper-calibration and universal no regret when best replying to forecasts in decision-making under uncertainty.

Use of AI is a valuable tool for weather prediction but only when it's trained with ample data, experts say Mon 18 May 2026 08.00 EDTLast modified on Mon 18 May 2026 08.01 EDT As the US prepares for hurricane season and a summer of record-breaking heat, experts fear the Trump administration's cuts to climate and weather data programming could make the federal government's weather forecasts less reliable when they are needed most. The National Oceanic and Atmospheric Administration (Noaa) late last year launched a suite of artificial intelligence-powered global weather forecast models which it said would improve "speed, efficiency, and accuracy". In March, an agency official said those models are being trained with centuries of weather data. Artificial intelligence is a valuable tool for weather prediction, but only when it is well-trained with ample data, said Monica Medina, who served as Noaa's principal deputy undersecretary of commerce for oceans and atmosphere from 2009 to 2012. Under Trump, climate and weather data collection has declined, said Medina.

We study online prediction under distribution shift, where inputs arrive chronologically and outcomes are revealed only after prediction. In this setting, predictors must remain stable in quiet regimes yet adapt when regimes shift, and the right adaptation memory is unknown in advance. We propose MELO (Memory-hedged Exponentially Weighted Least-Squares Online aggregation), a model-agnostic method that hedges across adaptation scales: it wraps any non-anticipating base-predictor pool with exponentially weighted least-squares (EWLS) adaptation experts at multiple forgetting factors, and aggregates raw and EWLS-adapted forecasts with MLpol which is a parameter-free online aggregation rule. Under boundedness conditions, we establish deterministic oracle inequalities showing that it competes with both the best raw predictor and the best bounded, time-varying affine combinations of the base predictions, up to a path-length-dependent tracking cost and a sublinear aggregation overhead. We evaluate MELO on French national electricity-load forecasting through the COVID-19 lockdown using no regime indicators, lockdown dates, or policy covariates. MELO reduces overall RMSE by 34.7%relative to base-only MLpol and achieves lower overall RMSE than a TabICL reference supplied with an external COVID policy-response covariate. MELO requires only lightweight per-step recursive updates without model retraining.

In this paper, we introduce the forecast reconciliation packages FoReco and FoRecoML for R (RCore Team 2026). Forecast reconciliation adjusts forecasts for linearly constrained multiple time series (such as hierarchical or grouped series, or series observed at different temporal frequencies) so that they are coherent with respect to the underlying constraints, improving both accuracy and consistency for informed decision making. The contributions of the packages are threefold. First, FoReco and FoRecoML are the first to offer functionality for forecast reconciliation methods across cross-sectional, temporal and cross-temporal frameworks. Second, the packages provide a comprehensive set of forecast reconciliation approaches, including classical (e.g., top-down, bottom-up and middle-out) and regression based reconciliation methods - in FoReco - as well as non-linear reconciliation methods using machine learning - in FoRecoML. A third key contribution is their unified design, which enables easy-to-use forecast reconciliation functions built on the same philosophy, regardless of the reconciliation framework or method.

In this section, we provide and expand upon a toy example. Recall that the inputs x and x0 need not correspond to real users but could instead represent hypothetical users. Example 5. Suppose that the regulatory guideline requires that users in the same geographical location receive similar weather forecasts. This can be written as "the weather forecasts that are selected by F should be similar for all users in the same geographical location", and S could be a randomly generated set of user pairs, where each pair corresponds to two (hypothetical) users in the same geographical location, and S could contain pairs across many locations. In the left-most panel, a filtering algorithm F takes in counterfactual inputs x and x0 and produces the content Z and Z0. Because a counterfactual regulation requires that F behave similarly under x and x0, the regulation is effectively requiring that content Z and Z0 are sufficiently similar (or, graphically, that they are close in Z). The question of how to quantify "similarity" is addressed in Section 2.1. The toy example in Example 5 is illustrated in the right-most panel.