Resource-Constrained Adaptive Inference for Sequential Pricing
For sequential pricing under resource constraints, this work provides a theoretical framework and practical algorithm to ensure valid inference when fixed-price inference is impossible.
The paper formalizes a support-exclusion failure in resource-constrained pricing where the controller's resource state can remove target price neighborhoods from the feasible set, and designs a target-aware pricing controller that certifies feasible target bands and logs continuous local densities, achieving polynomial regret-information rates with polynomial target mass.
Resource-constrained pricing controllers can make fixed-price inference impossible: the controller's resource state may remove the target price neighborhood from the feasible set, even when every realized action has a known positive density. We formalize this support-exclusion failure through a local non-identification result and a realized information clock. We then design a target-aware pricing controller that certifies feasible target bands and logs continuous local densities. Localized debiasing gives studentized intervals whose width is governed by this clock. The resulting regret--information accounting, stated up to pilot re-solving error, shows that cheap exploration can be insufficient for inference: polynomial target mass gives polynomial rates, while a pure $1/t$ target branch does not yield shrinking fixed-target intervals without additional local movement. Experiments show calibration in certified bands and diagnostic abstention when the resource state collapses target support.