We study a sequential profit-maximization problem, optimizing for both price and ancillary variables like marketing expenditures. Specifically, we aim to maximize profit over an arbitrary sequence of multiple demand curves, each dependent on a distinct ancillary variable, but sharing the same price. A prototypical example is targeted marketing, where a firm (seller) wishes to sell a product over multiple markets. The firm may invest different marketing expenditures for different markets to optimize customer acquisition, but must maintain the same price across all markets. Moreover, markets may have heterogeneous demand curves, each responding to prices and marketing expenditures differently. The firm's objective is to maximize its gross profit, the total revenue minus marketing costs. Our results are near-optimal algorithms for this class of problems in an adversarial bandit setting, where demand curves are arbitrary non-adaptive sequences, and the firm observes only noisy evaluations of chosen points on the demand curves. For $n$ demand curves (markets), we prove a regret upper bound of $\tilde{O}(nT^{3/4})$ and a lower bound of $\Omega((nT)^{3/4})$ for monotonic demand curves, and a regret bound of $\tilde{\Theta}(nT^{2/3})$ for demands curves that are monotonic in price and concave in the ancillary variables.

Artificial intelligence and machine learning continue to increase the stakes in the analytic, predictive and executional arms race needed to create and keep customer relationships. Marketing is at the center of this change, and several existing applications promise to irrevocably change the landscape with step-level superpowers. With great power comes great responsibility, and marketers must be ready to change and adapt to the new landscape if they want to avoid being the haphazard hero who lost the instructions to their supersuit. By recognizing the four ways AI and machine learning will enable change in industries and organizations, the savvy marketer can avoid costly missteps as they learn how to harness the awesome power of an enhanced world. Chances are you are already using AI and machine learning to buy media.

Some people think I am a machine learning expert. And in some ways, I am, which is great, because it is suddenly the flavor of the week--and I have lots of companies asking me for help solving their marketing problems with this new secret sauce. What I know is less how machine learning works, and more how to know that machine learning will help you with your marketing problem. What I don't know is all how all of the lovely algorithms in the picture above actually work. And you don't need to, either.