Generative Multi-Flow Networks: Centralized, Independent and Conservation

Generative flow networks utilize the flow matching loss to learn a stochastic policy for generating objects from a sequence of actions, such that the probability of generating a pattern can be proportional to the corresponding given reward. However, existing works can only handle single flow model tasks and cannot directly generalize to multi-agent flow networks due to limitations such as flow estimation complexity and independent sampling. In this paper, we propose the framework of generative multi-flow networks (GMFlowNets) that can be applied to multiple agents to generate objects collaboratively through a series of joint actions. Then, the centralized flow network algorithm is proposed for centralized training GMFlowNets, while the independent flow network algorithm is proposed to achieve decentralized execution of GMFlowNets. Based on the independent global conservation condition, the flow conservation network algorithm is then proposed to realize centralized training with decentralized execution paradigm. Theoretical analysis proves that using the multi-flow matching loss function can train a unique Markovian flow, and the flow conservation network can ensure independent policies can generate samples with probability proportional to the reward function. Experimental results demonstrate the performance superiority of the proposed algorithms compared to reinforcement learning and MCMC-based methods.