Ambiguous Probabilistic Programs

Probabilistic programs are widely used decision models. When implemented in practice, however, there often exists distributional ambiguity in these models. In this paper, we model the ambiguity using the likelihood ratio (LR) and use LR to construct various ambiguity sets. We consider ambiguous probabilistic programs which optimize under the worst case. Ambiguous probabilistic programs can be classified as ambiguous probability minimization problems (PM) and ambiguous chance constrained programs (CCP). We show that the ambiguous PM can be transformed to a pure PM under the nominal distribution, and that the ambiguous CCP can be transformed to a pure CCP with only the confidence level being rescaled from the original CCP. Our study indicates that ambiguous probabilistic programs with ambiguity modeled by LR essentially have the same complexity as the corresponding pure probabilistic programs and that risk and uncertainty have strong connections in probabilistic programs.



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