Multivariable Feedback Control for Multiconstraint Optimization in Online Advertising

Online advertising is typically implemented via real-time bidding, and advertising campaigns are then defined as extremely high-dimensional optimization problems. To solve these problems in light of large scale and significant uncertainties, the optimization problems are modularized in a manner that makes feedback control a critical component of the solution. The control problem, however, is challenging due to plant uncertainties, nonlinearities, time-variance, and noise. Multi-constraint optimization problems are especially difficult to solve via feedback control because of the dynamic interaction across feedback loops. This paper demonstrates how one particular multi-constraint problem can be solved using a cascade feedback controller. The inner loop is managed by a linear time-periodic feedforward controller combined with a linear time-invariant feedback controller. Meanwhile, the outer loop is managed by a linear time-invariant feedforwardfeed-back controller. This paper is concerned with the outer loop controller and derives sufficient conditions for stability of the nonlinear closed loop system by expressing it as a Lure system and by engaging the circle criterion. The solution is evaluated in a simulated environment based on artificial data.