In display advertising, advertisers want to achieve a marketing objective with constraints on budget and cost-per-outcome. This is usually formulated as an optimization problem that maximizes the total utility under constraints. The optimization is carried out in an online fashion in the dual space - for an incoming Ad auction, a bid is placed using an optimal bidding formula, assuming optimal values for the dual variables; based on the outcome of the previous auctions, the dual variables are updated in an online fashion. While this approach is theoretically sound, in practice, the dual variables are not optimal from the beginning, but rather converge over time. Specifically, for the cost-constraint, the convergence is asymptotic. As a result, we find that cost-control is ineffective. In this work, we analyse the shortcomings of the optimal bidding formula and propose a modification that deviates from the theoretical derivation. We simulate various practical scenarios and study the cost-control behaviors of the two algorithms. Through a large-scale evaluation on the real-word data, we show that the proposed modification reduces the cost violations by 50%, thereby achieving a better cost-control than the theoretical bidding formula.

We establish a general optimization framework for the design of automated bidding agent in dynamic online marketplaces. It optimizes solely for the buyer's interest and is agnostic to the auction mechanism imposed by the seller. As a result, the framework allows, for instance, the joint optimization of a group of ads across multiple platforms each running its own auction format. Bidding strategy derived from this framework automatically guarantees the optimality of budget allocation across ad units and platforms. Common constraints such as budget delivery schedule, return on investments and guaranteed results, directly translates to additional parameters in the bidding formula. We share practical learnings of the deployed bidding system in the LinkedIn ad marketplace based on this framework.