Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization

Опубликовано 17 августа 2016, 22:00

Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this talk, I will introduce the new concept of adaptive submodularity, generalizing the classical notion of submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. I will illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse applications including sensor selection, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases and handle natural generalizations. In an application to Bayesian experimental design, we show how greedy optimization of a novel adaptive submodular criterion outperforms standard myopic techniques such as information gain and value of information.