Adaptive Inference for Resource-Constrained Dynamic Pricing

arXiv:2606.03736v2 Announce Type: replace-cross Abstract: We study resource-constrained dynamic pricing when the seller seeks revenue and valid inference about demand at a price fixed before the selling season. Depletion can remove every feasible price near the target, so randomization over the remaining prices need not preserve identification. We propose an inference-aware re-solving policy that checks target support before observing the current covariates and implements the fluid target load with a logged pricing mixture. In an affine binding-capacity family, target mass $t^{-\gamma}$ yields information $T^{1-\gamma}$, interval radius $T^{-(1-\gamma)/2}$, and regret $O(\log T+T^{1-\gamma})$ against the initial fluid optimum. In the same affine family, learned barycentric re-solving retains a target-local component of constant mass and, with polynomial error spending of exponent greater than one, achieves a linear information clock and $O(\log T)$ regret; slack-capacity local pricing gives the same orders. An exact-input smooth-frontier extension gives root-$T$ inference and $O(\log^2T)$ regret. Physical exclusion rules out uniformly shrinking intervals, while target mass of order $1/t$ alone yields bounded information. The policy reports an interval only after its prespecified support and information checks pass.

Abstract:We study resource-constrained dynamic pricing when the seller seeks revenue and valid inference about demand at a price fixed before the selling season. Depletion can remove every feasible price near the target, so randomization over the remaining prices need not preserve identification. We propose an inference-aware re-solving policy that checks target support before observing the current covariates and implements the fluid target load with a logged pricing mixture. In an affine binding-capacity family, target mass $t^{-\gamma}$ yields information $T^{1-\gamma}$, interval radius $T^{-(1-\gamma)/2}$, and regret $O(\log T+T^{1-\gamma})$ against the initial fluid optimum. In the same affine family, learned barycentric re-solving retains a target-local component of constant mass and, with polynomial error spending of exponent greater than one, achieves a linear information clock and $O(\log T)$ regret; slack-capacity local pricing gives the same orders. An exact-input smooth-frontier extension gives root-$T$ inference and $O(\log^2T)$ regret. Physical exclusion rules out uniformly shrinking intervals, while target mass of order $1/t$ alone yields bounded information. The policy reports an interval only after its prespecified support and information checks pass.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2606.03736 [stat.ML]

(or arXiv:2606.03736v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2606.03736 Focus to learn more arXiv-issued DOI via DataCite

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Adaptive Inference for Resource-Constrained Dynamic Pricing

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