Adaptive Inference for Resource-Constrained Dynamic Pricing

Abstract

We study dynamic pricing over a finite selling horizon when limited resource capacity determines revenue and the observations available for inference at a prespecified price. Resource depletion can remove the target neighborhood from the feasible price set, changing the experiment generated by the pricing policy. We develop inference-aware re-solving controllers that check target-band feasibility before current covariates arrive and log the pricing mixture. Target-reserved and smooth controllers take population mean-pair geometry as a predeployment input; learned barycentric re-solving instead estimates stationary mean-consumption vectors of predeclared component kernels. On an affine binding-capacity family, an exact-input target-reserved controller assigning mass $t^{-\gamma}$ obtains an information clock of order $T^{1-\gamma}$ in probability, radius $O_p\{T^{-(1-\gamma)/2}\}$, and, under an exposed-face reward identity, a signed fluid-benchmark gap bounded above by $O(\log T+T^{1-\gamma})$. Under the exogenous affine-face condition, predeclared target support, and polynomial error spending with exponent greater than one, learned barycentric re-solving has a linear information clock in probability and an $O(\log T)$ signed-gap upper bound; centered local pricing has the same orders under slack capacity and global target optimality. An exact-input, target-compatible smooth alternative without reservation gives a linear clock in probability, an $O_p(T^{-1/2})$ deterministic-envelope radius with unconditional coverage and reporting probability tending to one, and an $O(\log^2 T)$ signed-gap upper bound. Boundary results show when physical support is lost and why a $1/t$ target branch yields only $O_p(1)$ information if it is the sole target-local source. The policy reports an interval when its prespecified support and information conditions hold and otherwise abstains.