Defines exact adaptivity gaps of e/(e-1) and 2 between policy classes for two-sided assortment optimization and provides 1/4-approximation for adaptive one-by-one policies plus 0.067-approximation for simultaneous policies under MNL, with extensions to constrained settings.
2010), where λ† is a feasible solution of max λ≥0 (X j∈S X C⊆C fj(C) · λj,C : X C⊆C λj,C = 1, ∀j ∈ S, X C:C∋i λj,C = x† ij, ∀i ∈ C, j ∈ S )
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Two-sided Assortment Optimization: Adaptivity Gaps and Approximation Algorithms
Defines exact adaptivity gaps of e/(e-1) and 2 between policy classes for two-sided assortment optimization and provides 1/4-approximation for adaptive one-by-one policies plus 0.067-approximation for simultaneous policies under MNL, with extensions to constrained settings.