Proves NP-hardness of computing decision-relevant dimension d* and coNP-hardness of global sufficiency in linear optimization, then gives poly-time pointwise algorithms, a cumulative compression scheme of size at most d*, and PAC bounds scaling with d* for contextual linear optimization.
(iv) The first statement follows since each variable gadget offers exactly two disjoint choices and each clause gadget offers exactly three disjoint choices
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Learning Decision-Sufficient Representations for Linear Optimization
Proves NP-hardness of computing decision-relevant dimension d* and coNP-hardness of global sufficiency in linear optimization, then gives poly-time pointwise algorithms, a cumulative compression scheme of size at most d*, and PAC bounds scaling with d* for contextual linear optimization.