Human in the Loop Adaptive Optimization for Improved Time Series Forecasting

TL;DR

This paper introduces a model-agnostic post-training adaptive optimization framework that enhances time-series forecasts without retraining by applying expressive, transform-based corrections to outputs. It combines automated action-based augmentation with optional human-in-the-loop corrections, where natural language feedback is translated into actionable transformations via an LLM, and supports inference-time optimization through discrete actions and continuous parameters. The approach is theoretically grounded in affine correction guarantees that reduce mean squared error and is validated across diverse datasets (e.g., electricity, weather, traffic) and forecasting models, showing consistent improvements with minimal overhead. The work also provides an interactive demo, a detailed empirical comparison of optimization strategies, and extensive supplementary material for reproducibility and extension, highlighting practical impact for real-time forecasting systems.

Abstract

Time series forecasting models often produce systematic, predictable errors even in critical domains such as energy, finance, and healthcare. We introduce a novel post training adaptive optimization framework that improves forecast accuracy without retraining or architectural changes. Our method automatically applies expressive transformations optimized via reinforcement learning, contextual bandits, or genetic algorithms to correct model outputs in a lightweight and model agnostic way. Theoretically, we prove that affine corrections always reduce the mean squared error; practically, we extend this idea with dynamic action based optimization. The framework also supports an optional human in the loop component: domain experts can guide corrections using natural language, which is parsed into actions by a language model. Across multiple benchmarks (e.g., electricity, weather, traffic), we observe consistent accuracy gains with minimal computational overhead. Our interactive demo shows the framework's real time usability. By combining automated post hoc refinement with interpretable and extensible mechanisms, our approach offers a powerful new direction for practical forecasting systems.

Figures (10)

• Figure 1: Overview of the forecasting pipeline: the initial model generates predictions from input $X$, which are refined by an action selection mechanism and optionally adjusted using human feedback interpreted by a language model (LLM), yielding the final output $Y$.
• Figure 3: Illustration of the effect of affine post-training correction on ridge regression forecasts. The model is trained on a synthetic linear target. Results shown for $100$ samples, $100$ validation points, and $10{,}000$ test points.
• Figure 4: Examples of learned post-training actions. Each transformation operates on the model’s forecast to reduce prediction error. Full action definitions are in Appendix \ref{['sec:definition_actions']}.
• Figure 5: Transformation pipeline: From user prompt to executable code.
• Figure 6: (a) Initial prediction vs. human-refined forecast. (b) Action code generated from natural language via LLM (qwen2-72b-32k). (c) RMSE improvement post-feedback.

Theorems & Definitions (2)

• Theorem 1: Affine Correction Reduces MSE
• Remark 1: On the Evaluation Metric for Post-Training