Establishes equivalence conditions between nested and joint risk assessments in contextual optimization, shows policy independence from contextual risk measure under conditions, and proves SAA consistency in RKHS.
Lemma A.2 (Lemma 1 in [42]) Consider a Polish space Z with Borel field B(Z) and a prob- ability space (Ω, F , P)
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Risk-averse Decision Making with Contextual Information: Model, Sample Average Approximation, and Kernelization
Establishes equivalence conditions between nested and joint risk assessments in contextual optimization, shows policy independence from contextual risk measure under conditions, and proves SAA consistency in RKHS.