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.
Define the feature map Ψaff(ξ, x) := " ⃗ (L⊤ U⋆x)ξ⊤ c⊤ 0 x # ∈R d⋆p+1, w B,b := ⃗(B) b ∈R d⋆p+1
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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.