Adaptive Automatic Model Selection for Demand Forecasting under Heterogeneous Demand Patterns

We study the problem of model selection among probabilistic forecasting models evaluated on datasets of multiple time series. The performance of a model on a single time series is quantified by the average value (score) of a proper scoring rule over a test set, but extending model selection to data sets of time series requires aggregating these scores. Common approaches either rely on scaling scores and averaging them (mean scaled score) or avoid scaling by using alternative statistics such as mean ranks or win rates. However, these approaches can yield conflicting conclusions. We show that such discrepancies arise from the skewness of the distribution of the scores, which is particularly pronounced when test sets are short. The skewness can cause non-mean criteria (e.g., mean rank, median, win rate) to select misspecified models. In contrast, the mean score is immune from this problem. We further show that, as the size of the test sets increases, all aggregation criteria converge to the same model selection decision, mitigating these discrepancies. Our experiments on intermittent demand time series, including data from the M5 competition, highlight the importance of sufficiently large test sets; the mean scaled score appears to be the more reliable approach, also because empirically we found its decision to remain consistent when different scaling factors are adopted.

Large-scale retail and industrial forecasting systems contain many heterogeneous time series whose lifecycle, sparsity, volatility, seasonality, spectral patterns, and contextual sensitivity differ substantially. A single forecasting model rarely performs well across all regimes, while dense ensembles increase inference cost and provide limited insight into expert suitability. This paper studies forecastability-aware expert routing: learning how data characteristics determine the suitability of forecasting experts. We propose \method{}, a sparse mixture-of-experts framework that represents each series with a multidimensional forecastability fingerprint, mines expert-suitability targets from validation performance, and trains a cost-aware sparse router to activate a small budgeted set of experts for each series. Using a production-scale vending-machine sales dataset from Shandong New Beiyang (SNBC), where the forecasting component has been integrated into the replenishment-planning pipeline, together with public retail benchmarks, we show that expert suitability varies systematically across data regimes. On the industrial dataset with 5,000+ machines and 60M+ transactions, \method{} Top-2 reduces MSE by 12.4% over the strongest single expert, LightGBM, while executing 1.92 experts per series on average. The deployed component produces demand forecasts, while inventory-oriented gains are estimated by an offline replay simulator under a fixed replenishment policy rather than by online intervention. The framework turns heterogeneous sales forecasting from heuristic model selection into data mining of forecastability patterns and expert specialization. Code is available at https://github.com/hit636/FAME

Retail demand forecasting remains difficult when demand shifts faster than static forecasting models can be retrained, especially in early demand cycles where newly observed labels are sparse. To address this, this study aims to improve adaptive retail forecasting by proposing a predict-then-correct (PtC) framework that retains a first-stage machine learning (ML) forecast and applies a few-shot continuous contextual bandit correction policy with similar-SKUs augmentation and top-p masked updating. Across Walmart retail data and an exclusive beverage dataset, PtC delivers statistically significant reductions in MAPE, MAE, and RMSE across stable & high volume, stable & low volume, and erratic & intermittent demand patterns, improves average RMSE by 9.52% over the ML-only baseline in the ablation study, and yields lower inventory costs than base-stock, proximal policy optimization, and soft actor-critic policies under the tested lead-time settings. These findings show that online forecast correction can bridge offline demand learning and real-time retail decision-making by adapting to sparse feedback without fully retraining the base forecasting model.