We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove linear convergence of the algorithm with respect to the ...
We investigate the use of entropy-regularized optimal transport (EOT) cost in developing generative models to learn implicit distributions. Two generative models are proposed. One uses EOT cost directly in an one-shot optimization problem and the other uses EOT cost iteratively in an adversarial game...
Next, we will outline how to derive our novel entropy regularized TRPO. First, by regularizing the KL divergence with Shannon entropy, the original TRPO (12) is reformulated into the following constrained maximization problem: (37)maxEˆtπθ(at|st)πθold(at|st)Aˆts.t.Eˆt[DKL(π...
Optimal transportRandomized shortest pathsDistances between nodesThe present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into a set of input ...
The "proximity" between probability laws is quantified by the Wasserstein distance, a notion pertaining to optimal transport theory. The combination of the classical entropic regularization technique in this field with recent results from convex duality theory allows to reformulate the distributionally ...
Now, we define an optimization problem that is equivalent to the entropy-regularized optimal transport as follows: minimize ∫ ∥ x − y ∥ 2 π ( x , y ) d x d y − 4 λ Ent ( π ) subject to ∫ π ( x , y ) d x = q ( y ) for ∀ y ∈ R n , (20) ...