Adaptive Inference for Resource-Constrained Dynamic Pricing

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 $O({\log }^{2}T)$ 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.