Budget optimization for online campaigns with positive carryover effects

While it is relatively easy to start an online advertising campaign, proper allocation of the marketing budget is far from trivial. A major challenge faced by the marketers attempting to optimize their campaigns is in the sheer number of variables involved, the many individual decisions they make in fixing or changing these variables, and the nontrivial short and long-term interplay among these variables and decisions. In this paper, we study interactions among individual advertising decisions using a Markov model of user behavior. We formulate the budget allocation task of an advertiser as a constrained optimal control problem for a Markov Decision Process (MDP). Using the theory of constrained MDPs, a simple LP algorithm yields the optimal solution. Our main result is that, under a reasonable assumption that online advertising has positive carryover effects on the propensity and the form of user interactions with the same advertiser in the future, there is a simple greedy algorithm for the budget allocation with the worst-case running time cubic in the number of model states (potential advertising keywords) and an efficient parallel implementation in a distributed computing framework like MapReduce. Using real-world anonymized datasets from sponsored search advertising campaigns of several advertisers, we evaluate performance of the proposed budget allocation algorithm, and show that the greedy algorithm performs well compared to the optimal LP solution on these datasets and that both show consistent 5-10% improvement in the expected revenue against the optimal baseline algorithm ignoring carryover effects.