The paper investigates Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known only up to a normalisation constant. It demonstrates that for strongly log-concave targets satisfying certain curvature conditions, WFR flows preserve strong log-concavity—unlike pure Wasserstein flows, which only do so in the Gaussian case. Leveraging this property, the authors derive explicit non-asymptotic convergence rates for the symmetrised Kullback-Leibler divergence, showing an additive decomposition into Wasserstein and Fisher‑Rao contributions and eliminating the need for a warm start.
By Francesca Romana Crucinio, Sahani Pathiraja
arXiv:2511.18060v3 Announce Type: replace-cross
Abstract: Wasserstein-Fisher-Rao (WFR) gradient flows have been recently proposed as a powerful sampling tool that combines the advantages of pure Wass...
By Francesca Romana Crucinio, Sahani Pathiraja
The paper investigates a natural gradient method based on the Fisher information matrix of state-action distributions, which follows a Fisher‑Rao gradient flow within the state-action polytope under a linear potential. It establishes linear convergence rates for Fisher‑Rao gradient flows of linear programs, with the rate tied to the program’s geometry, and provides improved error bounds for entropic regularization. Additionally, the authors extend their analysis to perturbed flows, proving sublinear convergence for both perturbed Fisher‑Rao and natural gradient flows, thereby encompassing state‑action natural policy gradients.
By Johannes M\"uller, Semih \c{C}ayc{\i}, Guido Mont\'ufar
The paper introduces a geometric framework for reinforcement learning that treats policies as mappings into the Wasserstein space of action probabilities. It establishes a Riemannian structure induced by stationary distributions, defines the tangent space of policies, and characterizes geodesics while addressing measurability concerns. The authors formulate a general RL optimization problem, construct a gradient flow via Otto's calculus, compute the gradient and Hessian of the energy, and demonstrate the approach with numerical examples for low‑dimensional problems and neural‑network‑parameterized policies for high‑dimensional settings.
By Mathias Dus (IRMA)
arXiv:2608. 03967v1 Announce Type: cross Abstract: Generative Flow Networks (GFlowNets) have emerged as a flexible framework for amortised inference over discrete and mixed discrete-continuous objects, requiring only an unnormalised target density specified through a reward.
By Yordan Raykov, Rodrigo Veiga
arXiv:2411. 00214v2 Announce Type: replace-cross Abstract: Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algorithms targeting the exclusive (reverse) KL divergence are rarely studied with such tools.
By Jia-Jie Zhu