Signal from Structure: Exploiting Submodular Upper Bounds in Generative Flow Networks

TL;DR

This paper introduces SUBo-GFN, a novel method leveraging submodular upper bounds to improve generative flow networks, enabling more efficient data generation for submodular reward-based tasks.

Contribution

It presents a new approach that exploits submodular structure to enhance GFlowNet training and performance, with theoretical analysis and empirical validation.

Findings

SUBo-GFN generates significantly more data than classical GFNs for the same query budget.

The method effectively matches distributions and produces high-quality candidates.

The approach is validated on synthetic and real-world submodular tasks.

Abstract

Generative Flow Networks (GFlowNets; GFNs) are a class of generative models that learn to sample compositional objects proportionally to their a priori unknown value, their reward. We focus on the case where the reward has a specified, actionable structure, namely that it is submodular. We show submodularity can be harnessed to retrieve upper bounds on the reward of compositional objects that have not yet been observed. We provide in-depth analyses of the probability of such bounds occurring, as well as how many unobserved compositional objects can be covered by a bound. Following the Optimism in the Face of Uncertainty principle, we then introduce SUBo-GFN, which uses the submodular upper bounds to train a GFN. We show that SUBo-GFN generates orders of magnitude more training data than classical GFNs for the same number of queries to the reward function. We demonstrate the effectiveness of SUBo-GFN in terms of distribution matching and high-quality candidate generation on synthetic and real-world submodular tasks.