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For a minimization problem, SDDP obtains a statistical UB in the forward pass. Can the statistical UB of SDDP be smaller than LB? I observed this phenomenon in the experiment, yet I'm not sure if it's possible or if it's just a bug.

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Yes. The upper bound is a confidence interval for the mean of the Monte Carlo simulation. You should expect that the confidence interval of a "lucky" Monte Carlo simulation that sampled only low-cost scenarios could be below the deterministic lower bound.

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