ResearchResearch paperReinforcement Learning1 source · Oct 13, 2026

Stein Variational Distributional Reinforcement Learning: Score-Guided Particles for Multivariate Return Distributions

We propose Stein variational distributional RL (SVDRL).

Key points

  • Decisions that weigh several reward signals against each other require the joint distribution of the return vector.
  • Multivariate distributional critics therefore represent each return distribution by M equal-weight particles trained with a discrepancy loss.
  • Its critic outputs Stein particles, which Stein variational gradient descent transports along a learned score field of the distributional Bellman target.
  • We learn this field by bootstrapped denoising score matching across noise levels and tie it across the Bellman recursion by a consistency loss, which we prove is a non-expansive temporal-difference scheme in score space.

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