Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue
We study contextual dynamic pricing with arbitrary covariate sequences and bounded, possibly nonbinary purchase quantities. Demand follows a semiparametric surplus-index model with an unknown linear valuation parameter and an unknown Hölder-smooth response. We impose neither concavity nor strong unimodality on revenue and allow nonunique optimal prices. We develop a pilot-corrected layered decision-partitioning policy that combines directional pilot estimation, local polynomial learning, predictable data assignment, and global action elimination. Pilot correction removes the first-order effect of valuation-parameter error, while permanent labels enable concentration under adaptive sampling. The policy attains the minimax smoothness-dependent horizon rate up to logarithmic factors; a matching lower bound already holds for a constant-context binary-demand subclass.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Minimax Optimality in Contextual Dynamic Pricing with General Valuation Models
Dynamic pricing, the practice of adjusting prices based on contextual factors, has gained significant attention due to its impact on revenue maximization. In this paper, we address the contextual dynamic pricing problem,…
Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning
We study contextual dynamic pricing in a semiparametric scalar-index valuation model where the latent value is $v_t=μ_\ast(\mathsf c_t)+ξ_t$, with an unknown utility map $μ_\ast$ and an unknown additive noise distributio…
Localized exploration in contextual dynamic pricing achieves dimension-free regret
We study the problem of contextual dynamic pricing with a linear demand model. We propose a novel localized exploration-then-commit (LetC) algorithm which starts with a pure exploration stage, followed by a refinement st…
Contextual Dynamic Pricing: Algorithms, Optimality, and Local Differential Privacy Constraints
We study contextual dynamic pricing problems where a firm sells products to $T$ sequentially-arriving consumers, behaving according to an unknown demand model. The firm aims to minimize its regret over a clairvoyant that…
Optimal Decision Rules when Payoffs are Partially Identified
We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter $\theta$ and the decision maker can use a point-identified parameter $\mu$ …