BiaWDRO: Controlling OOD Error in Offline Model-Based Optimization via Wasserstein Distributionally Robust Optimization

Offline model-based optimization (MBO) seeks to discover high-performing designs that maximize a black-box objective function using only pre-collected datasets, with applications such as materials discovery, biological sequence design, and robot morphology optimization. The central challenge in offline MBO is out-of-distribution (OOD) error, where surrogate models yield overconfident predictions that mislead the optimization process toward spurious optima. To mitigate this risk, conservative methods have emerged as a prevalent approach. However, these methods often rely on heuristic techniques. We introduce BiaWDRO, which adapts Wasserstein Distributionally Robust Optimization (DRO) to offline MBO by controlling worst-case predictive bias within Wasserstein ambiguity sets. Applying Lagrangian duality, we derive an objective that mitigates OOD overestimation through tractable adversarial perturbations of training samples. This approach establishes connections between DRO and conservative modeling, providing a principled approach that replaces previous heuristic methods. We further derive an explicit lower bound on empirical fitting error, quantifying the trade-off between worst-case predictive bias and fitting accuracy. Experiments on Design-Bench demonstrate competitive performance across diverse offline MBO tasks.