Stochastic Knapsack Revisited: The Service Level Perspective

A key challenge in the resource allocation problem is to find near-optimal policies to serve different customers with random demands/revenues, using a fixed pool of capacity (properly configured). Three classes of allocation policies, responsive (with perfect hindsight), adaptive (with information updates), and anticipative (with forecast information) policies, are widely used in practice. We analyze and compare the performances of these policies for both capacity minimization and revenue maximization models. In both models, the performance gaps between optimal anticipative policies and adaptive policies are shown to be bounded when the demand and revenue of each item are independently generated. In contrast, the gaps between the optimal adaptive policies and responsive policies can be arbitrarily large. More importantly, we show that the techniques developed, and the persistency values obtained from the optimal responsive policies can be used to design good adaptive and anticipative policies for the other two variants of resource allocation problems.

Learning Within an Instance for Designing High-Revenue Combinatorial Auctions

We develop a new framework for designing truthful, high-revenue (combinatorial) auctions for limited supply. Our mechanism learns within an instance. It generalizes and improves over previously-studied random-sampling mechanisms. It first samples a participatory group of bidders, then samples several learning groups of bidders from the remaining pool of bidders, learns a high-revenue auction from the learning groups, and finally runs that auction on the participatory group. Previous work on random-sampling mechanisms focused primarily on unlimited supply. Limited supply poses additional significant technical challenges, since allocations of items to bidders must be feasible. We prove guarantees on the performance of our mechanism based on a market-shrinkage term and a new complexity measure we coin partition discrepancy. Partition discrepancy simultaneously measures the intrinsic complexity of the mechanism class and the uniformity of the set of bidders. We then introduce new auction classes that can be parameterized in a way that does not depend on the number of bidders participating, and prove strong guarantees for these classes. We show how our mechanism can be implemented efficiently by leveraging practically-efficient routines for solving winner determination. Finally, we show how to use structural revenue maximization to decide what auction class to use with our framework when there is a constraint on the number of learning groups.