Towards Stable Machine Learning Model Retraining via Slowly Varying Sequences

Retraining machine learning models (ML) when new batches of data become available is an important task in real-world pipelines. Existing methods focus largely on greedy approaches to find the best-performing model for each batch, without considering the stability of the model's structure across retraining iterations. In this study, we propose a methodology for finding sequences of ML models that are stable across retraining iterations. We develop a mixed-integer optimization algorithm that is guaranteed to recover Pareto optimal models (in terms of the predictive power-stability trade-off) and an efficient polynomial-time algorithm that performs well in practice. Our method focuses on retaining consistent analytical insights -- which is important to model interpretability, ease of implementation, and fostering trust with users -- by using custom-defined distance metrics that can be directly incorporated into the optimization problem. Importantly, our method shows stronger stability than greedily trained models with a small, controllable sacrifice in model performance in a real-world case study. Using SHAP feature importance, we show that analytical insights are consistent across retraining iterations.