Generative Pretraining for Black-Box Optimization

Many problems in science and engineering involve optimizing an expensive black-box function over a high-dimensional space. For such black-box optimization (BBO) problems, we typically assume a small budget for online function evaluations, but also often have access to a fixed, offline dataset for pretraining. Prior approaches seek to utilize the offline data to approximate the function or its inverse but are not sufficiently accurate far from the data distribution. We propose Black-box Optimization Transformer (BOOMER), a generative framework for pretraining black-box optimizers using offline datasets. In BOOMER, we train an autoregressive model to imitate trajectory runs of implicit black-box function optimizers. Since these trajectories are unavailable by default, we develop a simple randomized heuristic to synthesize trajectories by sorting random points from offline data. We show theoretically that this heuristic induces trajectories that mimic transitions from diverse low-fidelity (exploration) to high-fidelity (exploitation) samples. Further, we introduce mechanisms to control the rate at which a trajectory transitions from exploration to exploitation, and use it to generalize outside the offline data at test-time. Empirically, we instantiate BOOMER using a casually masked Transformer and evaluate it on Design-Bench, where we rank the best on average, outperforming state-of-the-art baselines.