VBO-MI: A Differentiable Black-Box Optimization Framework via Variational Mutual Information Estimation

Farhad Mirkarimi

Many real-world tasks require optimizing expensive black-box functions accessible only through noisy evaluations, a setting commonly addressed with Bayesian optimization. While Gaussian processes(GPs) and Bayesian neural networks have driven significant progress, GP-based methods scale cubically with observations, and BNN-based approaches remain burdened by expensive posterior sampling such as Hamiltonian Monte Carlo, and inner-loop acquisition optimization in high-dimensional setting. In this work, we propose VBO-MI, a fully gradient-based BO framework that requires no assumptions on a Gaussian prior or a variational posterior family over $f$. While our framework uses gradient-based updates to train the internal action and information-estimation networks, it treats the objective function $f$ as a strict black box, requiring only zeroth-order evaluations. To enable end-to-end gradient flow, we employ an actor-critic architecture consisting of an action-net to navigate the input space and a variational critic to estimate a surrogate information signal for exploration. Additionally, we design a lightweight surrogate that approximates the objective from observed data using a replay…