An empirical KL minimizer over log-potentials estimates Schrödinger bridge potentials with terminal excess KL risk O(log^2 n / n) in the realizable case, even when the target distribution has unbounded support.
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Sample complexity of Schr\"odinger potential estimation
An empirical KL minimizer over log-potentials estimates Schrödinger bridge potentials with terminal excess KL risk O(log^2 n / n) in the realizable case, even when the target distribution has unbounded support.