Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based approaches rely primarily on generative models that yield exact sample likelihoods. This work introduces a method that lifts this restriction and opens the possibility to employ highly expressive latent variable models like diffusion models. Our approach is conceptually based on a loss that upper bounds the reverse Kullback-Leibler divergence and evades the requirement of exact sample likelihoods. We experimentally validate our approach in data-free Combinatorial Optimization and demonstrate that our method achieves a new state-of-the-art on a wide range of benchmark problems.

翻译：学习从离散集合上的难解分布中进行采样，且不依赖相应训练数据，是组合优化等广泛领域中的一个核心问题。目前流行的深度学习方法主要依赖于能够产生精确样本似然的生成模型。本文提出了一种方法，解除了这一限制，为使用扩散模型等高表达能力潜变量模型开辟了可能性。我们的方法在概念上基于一个上界反向Kullback-Leibler散度的损失函数，从而规避了对精确样本似然的要求。我们在无数据组合优化中通过实验验证了我们的方法，并证明其在广泛的基准问题上达到了新的最优性能。