Contextual Procurement Auctions with Bandit Learning

Abstract

We study repeated procurement auctions in which producers have private costs and the platform must learn the context-dependent value of selecting each producer. We evaluate performance by welfare regret: the cumulative loss in total surplus relative to the full-information efficient rule that knows the context-dependent values and true producer costs. The natural UCB allocation rule achieves $\widetilde O(\sqrt{ngT})$ welfare regret under truthful bids, but its adaptive, bid-dependent learning path does not by itself ensure truthfulness. To obtain exact incentives, we first design a bid-independent explore-then-commit mechanism with empirical threshold payments; it is dominant-strategy truthful and has $\widetilde O((ng)^{1/3}T^{2/3})$ regret. We then introduce frozen-payment UCB, which estimates payments from initial bid-independent exploration but continues allocation learning by UCB. Under a truthful-path margin condition, the frozen-payment UCB is approximately truthful with an average per-round deviation gain $\widetilde O(T^{-1/4})$ for fixed $n$, $g$. Under truthful bidding, it achieves $\widetilde O(\sqrt{ngT})$ welfare regret, matching the UCB rate. A lower bound shows that this regret-incentive tradeoff is tight within the frozen critical-payment class.