Simulating, Fast and Slow: Learning Policies for Black-Box Optimization

In recent years, solving optimization problems involving black-box simulators has become a point of focus for the machine learning community due to their ubiquity in science and engineering. The simulators describe a forward process fsim: (psi, x) rightarrow y from simulation parameters psi and input data x to observations y, and the goal of the optimization problem is to find parameters psi that minimize a desired loss function. Sophisticated optimization algorithms typically require gradient information regarding the forward process, fsim, with respect to the parameters psi. However, obtaining gradients from black-box simulators can often be prohibitively expensive or, in some cases, impossible. Furthermore, in many applications, practitioners aim to solve a set of related problems. Thus, starting the optimization ``ab initio", i.e. from scratch, each time might be inefficient if the forward model is expensive to evaluate. To address those challenges, this paper introduces a novel method for solving classes of similar black-box optimization problems by learning an active learning policy that guides a differentiable surrogate's training and uses the surrogate's gradients to optimize the simulation parameters with gradient descent. After training the policy, downstream optimization of problems involving black-box simulators requires up to ~90% fewer expensive simulator calls compared to baselines such as local surrogate-based approaches, numerical optimization, and Bayesian methods.