Discrete Probabilistic Inference as Control in Multi-path Environments (2402.10309v2)

Abstract: 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.

• The paper demonstrates that a revised reward structure unifies MaxEnt RL and GFlowNets for rigorous probabilistic inference.
• It establishes computational equivalence between the Path Consistency Learning (PCL) and Subtrajectory Balance objectives across structured sampling tasks.
• Empirical studies in Bayesian learning, factor graphs, and phylogenetic analysis validate the framework’s efficacy in correcting multipath-induced biases.

Bridging Between Maximum Entropy Reinforcement Learning and Generative Flow Networks

Overview

This work presents a formal and comprehensive analysis aiming at demystifying the mathematical and conceptual ties between Maximum Entropy Reinforcement Learning (MaxEnt RL) and Generative Flow Networks (GFlowNets). Through a series of theoretical assertions, the paper affirms that under certain modifications to the reward structure, the optimal policy distributions yielded by MaxEnt RL can align perfectly with those produced by GFlowNets, leading to a unified understanding across seemingly disparate fields of probabilistic inference and sequential decision-making.

Methodological Enhancements

At the heart of our quantitative assessment is the novel adaptation of the reward mechanism in the contexts of MaxEnt RL to correct bias arising from multiple pathways leading to identical outcomes in structured sampling problems. This correction ensures that the marginalized distribution over terminating states is proportional to the original intention, thereby maintaining fidelity to the Gibbs distribution regardless of the multipath environment's structured intricacy.

Equivalence Between Algorithms

The investigation further delineates the computational equivalence between specific algorithmic implementations within MaxEnt RL and GFlowNets under the adjusted reward schema. Notably, it highlights the proportional relationship between the Path Consistency Learning (PCL) objective in MaxEnt RL and the Subtrajectory Balance (SubTB) objective in GFlowNets. This equivalency, established through meticulous theoretical underpinning, extends to a broader array of algorithmic pairings, thereby underscoring a unified computational pathway towards achieving entropy-augmented probabilistic inference in structured environments.

Empirical Validation

Empirical analyses across diverse domains articulate the robustness and general applicability of the theoretical assertions made. By evaluating algorithmic performance within discrete factor graphs, Bayesian structure learning, and phylogenetic tree generation tasks, the paper substantiates the practical congruence between the optimized policy distributions derived from MaxEnt RL and GFlowNets. These experiments further validate that the adjusted reward framework effectively mitigates the bias induced by multipath generation dynamics, thereby aligning the terminating state distributions with the Gibbs distribution.

Theoretical Implications

The paper’s foundational contribution towards establishing a rigorous equivalence between MaxEnt RL and GFlowNets offers significant theoretical advancement. It elucidates that, under a unified reward correction mechanism, both paradigms can be perceived as different manifestations of the same underlying probabilistic inference process. This insight not only bridges gaps in literature but also harmonizes two robust yet seemingly divergent frameworks under the broader umbrella of sequential decision-making and probabilistic modeling.

Practical Relevance

On a practical note, understanding the nuanced interplay between MaxEnt RL and GFlowNets opens new avenues for algorithmic innovation and refinement. By leveraging the strengths of both approaches, researchers and practitioners can engineer more efficient, scalable, and accurate models for complex probabilistic inference tasks spanning various domains, from drug discovery and genomics to combinatorial optimization and beyond.

Future Directions

This work illuminates several pathways for future investigation, notably the extension of the established equivalence into continuous domains and the exploration of unified parametrization strategies for policy and state flow functions. Moreover, it beckons further inquiry into bridging other algorithmic variants and exploring the implications of these findings in more stochastic environments, thus broadening the horizon for advanced probabilistic modeling and inference techniques.

Conclusion

In sum, this paper makes a significant stride towards unifying MaxEnt RL and GFlowNets through a deep theoretical framework supported by empirical evidence. By presenting a coherent schema for correcting reward mechanisms in structured sampling problems, it paves the way for a new generation of models that leverage the best of both worlds for sophisticated probabilistic inference and decision-making tasks.