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An introductory study of Large Deviations upper bounds from a worst-case perspective under parameter uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging min-max (or max-min) problems that admitdoi:10.3906/mat-1607-20 fatcat:sr5ye2mrzbdqliyppjdqvfknw4