Discovering and Learning Probabilistic Models of Black-Box AI Capabilities

Black-box AI (BBAI) systems such as foundational models are increasingly being used for sequential decision making. To ensure that such systems are safe to operate and deploy, it is imperative to develop efficient methods that can provide a sound and interpretable representation of the BBAI's capabilities. This paper shows that PDDL-style representations can be used to efficiently learn and model an input BBAI's planning capabilities. It uses the Monte-Carlo tree search paradigm to systematically create test tasks, acquire data, and prune the hypothesis space of possible symbolic models. Learned models describe a BBAI's capabilities, the conditions under which they can be executed, and the possible outcomes of executing them along with their associated probabilities. Theoretical results show soundness, completeness and convergence of the learned models. Empirical results with multiple BBAI systems illustrate the scope, efficiency, and accuracy of the presented methods.

Optimal Transport for Probabilistic Circuits

We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our knowledge, there is no existing approach to compute the Wasserstein distance between probability distributions given by PCs. We consider a Wasserstein-type distance that restricts the coupling measure of the associated optimal transport problem to be a probabilistic circuit. We then develop an algorithm for computing this distance by solving a series of small linear programs and derive the circuit conditions under which this is tractable. Furthermore, we show that we can also retrieve the optimal transport plan between the PCs from the solutions to these linear programming problems. We then consider the empirical Wasserstein distance between a PC and a dataset, and show that we can estimate the PC parameters to minimize this distance through an efficient iterative algorithm.