  We consider the problem of sampling from a discrete and structured
distribution as a sequential decision problem, where the objective is to find a
stochastic policy such that objects are sampled at the end of this sequential
process proportionally to some predefined reward. While we could use maximum
entropy Reinforcement Learning (MaxEnt RL) to solve this problem for some
distributions, it has been shown that in general, the distribution over states
induced by the optimal policy may be biased in cases where there are multiple
ways to generate the same object. To address this issue, Generative Flow
Networks (GFlowNets) learn a stochastic policy that samples objects
proportionally to their reward by approximately enforcing a conservation of
flows across the whole Markov Decision Process (MDP). In this paper, we extend
recent methods correcting the reward in order to guarantee that the marginal
distribution induced by the optimal MaxEnt RL policy is proportional to the
original reward, regardless of the structure of the underlying MDP. We also
prove that some flow-matching objectives found in the GFlowNet literature are
in fact equivalent to well-established MaxEnt RL algorithms with a corrected
reward. Finally, we study empirically the performance of multiple MaxEnt RL and
GFlowNet algorithms on multiple problems involving sampling from discrete
distributions.
