We consider two robust versions of optimal transport, named $\textit{Robust Semi-constrained Optimal Transport}$ (RSOT) and $\textit{Robust Unconstrained Optimal Transport}$ (ROT), formulated by relaxing the marginal constraints with Kullback-Leibler divergence. For both problems in the discrete settings, we propose Sinkhorn-based algorithms that produce $\varepsilon$-approximations of RSOT and ROT in $\widetilde{\mathcal{O}}(\frac{n^2}{\varepsilon})$ time, where $n$ is the number of supports of the probability distributions... (read more)

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