Logarithmic Regret in Feature-based Dynamic Pricing
Dec 6, 2021
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Yu-Xiang Wang
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Feature-based dynamic pricing is an increasingly popular model of setting prices for highly differentiated products with applications in digital marketing, online sales, real estate and so on. The problem was formally studied as an online learning problem (Javanmard Nazerzadeh, 2019) where a seller needs to propose prices on the fly for a sequence of T products based on their features x while having a small regret relative to the best —"omniscient"— pricing strategy she could have come up with in hindsight. We revisit this problem and provide two algorithms (EMLP and ONSP) for stochastic and adversarial feature settings, respectively, and prove the optimal O(dlogT) regret bounds for both. In comparison, the best existing results are O(min{1/λ_min^2logT, √(T)}) and O(T^2/3) respectively, with λ_min being the smallest eigenvalue of 𝔼[xx^T] that could be arbitrarily close to 0. We also prove an Ω(√(T)) information-theoretic lower bound for a slightly more general setting, which demonstrates that “knowing-the-demand-curve” leads to an exponential improvement in feature-based dynamic pricing.Feature-based dynamic pricing is an increasingly popular model of setting prices for highly differentiated products with applications in digital marketing, online sales, real estate and so on. The problem was formally studied as an online learning problem (Javanmard Nazerzadeh, 2019) where a seller needs to propose prices on the fly for a sequence of T products based on their features x while having a small regret relative to the best —"omniscient"— pricing strategy she could have come up with i…
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NeurIPS 2021
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About NeurIPS 2021
Neural Information Processing Systems (NeurIPS) is a multi-track machine learning and computational neuroscience conference that includes invited talks, demonstrations, symposia and oral and poster presentations of refereed papers. Following the conference, there are workshops which provide a less formal setting.
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