High dimensional revenue management

Abstract

We present potential solutions to several problems that arise in making revenue management (RM) practical for online advertising and related modern applications. Principally, RM solutions for these problems must contend with (i) highly volatile demand processes that are hard to forecast, and (ii) massive scale that makes even basic optimization problems challenging. Our solutions to these problems are interesting in their own right in the areas of stochastic optimization, high dimensional learning and distributed optimization. In the first part of the thesis, we propose a model predictive control approach to combat volatile demand. This approach is conceptually simple, uses available demand data in a natural way, and, most importantly, can be shown to generate significant revenue advantages on real-world data from ad networks. Under mild restrictions, we prove that our algorithm achieves uniform relative performance guarantees vis-a-vis a clairvoyant in the face of arbitrary volatility, while simultaneously being optimal in the event that volatility is negligible. This is the first result of its kind for model predictive control. While our approach above is effective at hedging demand shocks that occur over "large" time horizons, it relies on the ability to estimate snapshots of the prevailing demand distribution over "short" time horizons. The second part of the thesis deals with learning the extremely high dimensional demand distributions that are typical in display advertising applications. This work exploits the special structure of the display advertising version of the NRM problem to achieve a sample complexity that scales gracefully in the dimensions of the problem. The third part of the thesis focuses on the problem of solving terabyte sized LPs on an hourly basis given a distributed computational infrastructure; solving these massive LPs is the computational primitive required to make our model predictive control approach practical. Here we design a linear optimization algorithm that fits a paradigm for distributed computation referred to as 'Map-Reduce'. An implementation of our solver in a shared memory environment where we can benchmark against solvers such as CPLEX shows that the algorithm outperforms those solvers on the types of LPs that an ad network would have to solve in practice.