An Algorithm for Stochastic Multiple-Choice Knapsack Problem and Keywords Bidding

We model budget-constrained keyword bidding in sponsored search auctions as a stochastic multiple-choice knapsack problem (S-MCKP) and propose a new algorithm to solve SMCKP and the corresponding bidding optimization problem. Our algorithm selects items online based on a threshold function which can be built/updated using historical data. Our algorithm achieved about 99% performance compared to the offline optimum when applied to a real bidding dataset. With synthetic dataset and iid item sets, its performance ratio against the offline optimum converges to one empirically with increasing number of periods.