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.

翻译：生成流网络（GFlowNets；GFNs）是一类生成模型，其学习按与先验未知值（即其奖励）成比例的方式采样组合对象。我们关注奖励具有特定、可操作结构的情形，即奖励是子模的。我们证明子模性可用于获取尚未观测到的组合对象的奖励上界。我们深入分析了此类界出现的概率，以及单个界能覆盖多少未观测的组合对象。遵循“面对不确定性保持乐观”原则，我们随后引入了SUBo-GFN，该模型利用子模上界训练GFN。我们证明，在相同奖励函数查询次数下，SUBo-GFN生成的训练数据量比经典GFNs高出数个数量级。我们在合成和真实世界的子模任务上，从分布匹配和高质量候选生成两方面验证了SUBo-GFN的有效性。