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We consider a retailer selling a single product with limited on-handinventory over a finite selling season. Customer demand arrives according to aPoisson process, the rate of which is influenced by a single action taken bythe retailer (such as price adjustment, sales commission, advertisementintensity, etc.). The relationship between the action and the demand rate isnot known in advance. However, the retailer is able to learn the optimal action"on the fly" as she maximizes her total expected revenue based on the observeddemand reactions.  Using the pricing problem as an example, we propose a dynamic"learning-while-doing" algorithm that only involves function value estimationto achieve a near-optimal performance. Our algorithm employs a series ofshrinking price intervals and iteratively tests prices within that intervalusing a set of carefully chosen parameters. We prove that the convergence rateof our algorithm is among the fastest of all possible algorithms in terms ofasymptotic "regret" (the relative loss comparing to the full informationoptimal solution). Our result closes the performance gaps between parametricand non-parametric learning and between a post-price mechanism and acustomer-bidding mechanism. Important managerial insight from this research isthat the values of information on both the parametric form of the demandfunction as well as each customer's exact reservation price are less importantthan prior literature suggests. Our results also suggest that firms would bebetter off to perform dynamic learning and action concurrently rather thansequentially.

Close the Gaps: A Learning-while-Doing Algorithm for a Class of Single-Product Revenue Management Problems