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 s–t unit-flow polytope X:= n x∈R p ≥0 : X a∈δ+(v) xa − X a∈δ−(v) xa = 1v=s, −1v=t, 0otherwise, o
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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.