Trajectory-Based Multi-Objective Hyperparameter Optimization for Model Retraining

Training machine learning models inherently involves a resource-intensive and noisy iterative learning procedure that allows epoch-wise monitoring of the model performance. However, in multi-objective hyperparameter optimization scenarios, the insights gained from the iterative learning procedure typically remain underutilized. We notice that tracking the model performance across multiple epochs under a hyperparameter setting creates a trajectory in the objective space and that trade-offs along the trajectories are often overlooked despite their potential to offer valuable insights to decision-making for model retraining. Therefore, in this study, we propose to enhance the multi-objective hyperparameter optimization problem by having training epochs as an additional decision variable to incorporate trajectory information. Correspondingly, we present a novel trajectory-based multi-objective Bayesian optimization algorithm characterized by two features: 1) an acquisition function that captures the improvement made by the predictive trajectory of any hyperparameter setting and 2) a multi-objective early stopping mechanism that determines when to terminate the trajectory to maximize epoch efficiency. Numerical experiments on diverse synthetic simulations and hyperparameter tuning benchmarks indicate that our algorithm outperforms the state-of-the-art multi-objective optimizers in both locating better trade-offs and tuning efficiency.