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.
The proof of Lemma 15 follows the same structure as the proof of Lemma 2, where we show that the LP in (3) is a relaxation of ( C-One-sided Adaptive) in the unconstrained setting
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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.