In a fixed-cost entropic optimal transport model with continuous cost and nonatomic marginals, compact-set large-deviation upper bounds do not extend to arbitrary closed sets, and no full LDP holds on the ambient space at speed 1/ε.
Weed,An explicit analysis of the entropic penalty in linear programming, Proceedings of the 31st Conference On Learning Theory, PMLR, vol
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Failure of ambient closed-set large-deviation upper bounds in entropic optimal transport
In a fixed-cost entropic optimal transport model with continuous cost and nonatomic marginals, compact-set large-deviation upper bounds do not extend to arbitrary closed sets, and no full LDP holds on the ambient space at speed 1/ε.