ResearchResearch paperReinforcement Learning1 source · Oct 12, 2026

DEFlow: Deep Equilibrium Flow Maximum-Entropy Reinforcement Learning

We introduce DEFlow, a deep equilibrium flow policy that replaces explicit Euler sampling with implicit Euler integration and solves all intermediate actions jointly as an equilibrium system.

Key points

  • Expressive flow policies can represent multiple high-value actions, but sampling them with few integration steps while retaining tractable action densities remains challenging.
  • We combine implicit differentiation with a discrete change-of-variables formula for the final-action density, enabling off-policy training within soft actor-critic without backpropagating through solver iterations.
  • DEFlow achieves an average relative improvement of approximately 10% in mean successful coverage over the strongest baseline across four Multi-Goal docking variants.
  • These results support implicit flow policies for tasks requiring both diversity and precision, at the cost of additional nonlinear and linear solves.

Sources (1)

  • [1]DEFlow: Deep Equilibrium Flow Maximum-Entropy Reinforcement Learning
    arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 12, 11:18 AM
    We introduce DEFlow, a deep equilibrium flow policy that replaces explicit Euler sampling with implicit Euler integration and solves all intermediate actions jointly as an equilibrium system.
    Expressive flow policies can represent multiple high-value actions, but sampling them with few integration steps while retaining tractable action densities remains challenging.

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