通过训练时正则化提升零售需求预测的稳定性，同时保持精度不变。
Accuracy-Preserving Stability Regularization for Large-Scale Retail Demand Forecasting
- 在训练中加入连续预测值间变化的惩罚项，增强时间序列预测路径稳定性。
- 在1000、3000、4000系列数据上，稳定度得分分别提升6.91%、6.66%、7.68%，RMSE变化小于0.72%。
- 适合需要稳定预测路径的零售运营场景，如补货与人力调度。
零售需求预测被用于补货、产能、人力和运输规划等多个环节。传统点误差目标不约束相邻预测间的突变，而事后平滑仅在模型拟合后生效。本文探讨在训练阶段对同系列连续预测值间的变动施加惩罚，是否能在不显著影响点精度的前提下提升横向预测路径的稳定性。该方法在结合近期需求嵌入与日历、价格、层级、商品及门店特征的时序结构化流程中验证。在选取的M5需求序列中，针对1000、3000和4000系列规模，该稳定性感知混合模型相比XGBoost分别提升预测稳定性评分6.91%、6.66%和7.68%，而RMSE变化均在0.72%以内（三组随机种子）。事后指数平滑虽降低原始波动，但导致更大的RMSE损失；训练时正则化在保持更高点精度的同时，在归一化稳定性下表现更优。研究将预测评估从单纯最小化点误差拓展至精度-稳定性权衡视角，适用于实际零售运营中的需求预测。
原文摘要 · Abstract (English)
Retail demand forecasts are reused across replenishment, capacity, labor, and transportation planning cycles. Point-error objectives do not constrain abrupt movement between adjacent forecasts, while post-hoc smoothing acts only after model fitting. We ask whether a training-time penalty on consecutive within-series movement can improve horizontal forecast-path stability without materially changing point accuracy. The penalty is evaluated in a temporal-structured pipeline combining recent-demand embeddings with calendar, price, hierarchy, item, and store features. On selected M5 demand series at 1000, 3000, and 4000-series scales, the stability-aware hybrid model improves Forecast Stability Score over XGBoost by 6.91%, 6.66%, and 7.68%, respectively, while RMSE changes remain within 0.72% across three random seeds. Post-hoc exponential smoothing attains lower raw movement but incurs a larger RMSE cost; training-time regularization preserves more point accuracy and performs favorably under normalized stability. These findings extend forecast evaluation from point-error minimization toward an accuracy-stability trade-off perspective for operational retail forecasting.
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