Cost-sensitive retraining via posterior learning debt

Model retraining is usually treated as an ongoing maintenance task. But as Harrison Katz now argues, retraining can be better understood as approximate Bayesian inference under computational constraints. The gap between a continuously updated belief state and your frozen deployed model is "learning debt," and the retraining decision is a cost minimization problem with a threshold that falls out of your loss function. In this article Katz provides a decision-theoretic framework for retraining policies. The result is evidence-based triggers that replace calendar schedules and make governance auditable. For readers less familiar with the Bayesian and decision-theoretic language, key terms are defined in a glossary at the end of the article.

Production machine learning systems degrade under concept drift, yet practitioners have little principled guidance on when to retrain. Retraining is costly, retraining budgets are finite, and a retrained model does not take effect instantly: training and deployment latency leave a stale model serving predictions while the data continues to move. We present a controlled empirical study of three practical model-refresh policies (periodic retraining, error-threshold triggering, and statistical drift-triggered retraining with ADWIN) against a no-retrain baseline, evaluated under a unified system model that makes retraining budgets and training-plus-deployment latency explicit. Across 3,933 experiment runs spanning three drift regimes, three budget levels, up to five latency levels, three datasets, and two learning modes, we find that the single most consequential design decision is not the retraining policy but whether the deployed model learns incrementally. With per-sample incremental updates, and for the linear online learner with immediate labels studied here, no policy differs from the no-retrain baseline by a practically significant margin in any of 54 paired comparisons, even at extreme latency. Without incremental updates, policy choice separates outcomes by 15-55 percentage points of post-drift accuracy, and simple periodic retraining significantly outperforms both reactive policies under abrupt and gradual drift, while reactive policies retain an advantage only under recurring drift. We document systematic failure modes of reactive policies and a latency-budget queueing interaction that silently halves effective retraining budgets, and release the full simulator, dataset pipelines, and per-run artifacts for reproducibility.

Sample-based generative models are increasingly used for probabilistic forecasting in high-stakes decision settings, yet their training objectives are blind to the decision maker's cost structure. These models are commonly trained with strictly proper scoring rules, such as the energy score, which allocate their training signal in proportion to data density, with no awareness of where forecast errors are most costly for downstream decisions. We therefore propose decision-aware training for sample-based generative models, augmenting the energy score objective with a differentiable decision loss that directly penalises the cost incurred by acting on the model's forecast. This combined loss is theoretically grounded, as the decision loss is itself a proper scoring rule. We validate our method on one synthetic and two real-world tasks, showing targeted improvements in cost-sensitive regions while retaining full probabilistic forecasts.