This article introduces a near-optimal bidding algorithm for use in real-time display advertising auctions. These auctions constitute a dominant distribution channel for internet display advertising and a potential funding model for addressable media. The proposed efficient, implementable learning algorithm is proven to rapidly converge to the optimal strategy while achieving zero regret and constituting a competitive equilibrium. This is the first algorithmic solution to the online knapsack problem to offer such theoretical guarantees without assuming a priori knowledge of object values or costs. Furthermore, it meets advertiser requirements by accommodating any valuation metric while satisfying budget constraints. Across a series of 100 simulated and 10 real-world campaigns, the algorithm delivers 98% of the value achievable with perfect foresight and outperforms the best available alternative by 11%. Finally, we show how the algorithm can be augmented to simultaneously estimate impression values and learn the bidding policy. Across a series of simulations, we show that the total regret delivered under this dual objective is less than that from any competing algorithm required only to learn the bidding policy.
Feedback Control of Real-Time Display Advertising