Non-monotone Submodular Maximization with Nearly Optimal Adaptivity and Query Complexity

Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an algorithm is governed by its adaptivity, which measures the number of sequential rounds needed if the algorithm can execute polynomially-many independent oracle queries in parallel. While low adaptivity is ideal, it is not sufficient for an algorithm to be efficient in practice---there are many applications of distributed submodular optimization where the number of function evaluations becomes prohibitively expensive. Motivated by these applications, we study the adaptivity and query complexity of submodular maximization. In this paper, we give the first constant-factor approximation algorithm for maximizing a non-monotone submodular function subject to a cardinality constraint $k$ that runs in $O(\log(n))$ adaptive rounds and makes $O(n \log(k))$ oracle queries in expectation. In our empirical study, we use three real-world applications to compare our algorithm with several benchmarks for non-monotone submodular maximization. The results demonstrate that our algorithm finds competitive solutions using significantly fewer rounds and queries.Comment: 12 pages, 8 figure

Scalable Methods for Adaptively Seeding a Social Network

In recent years, social networking platforms have developed into extraordinary channels for spreading and consuming information. Along with the rise of such infrastructure, there is continuous progress on techniques for spreading information effectively through influential users. In many applications, one is restricted to select influencers from a set of users who engaged with the topic being promoted, and due to the structure of social networks, these users often rank low in terms of their influence potential. An alternative approach one can consider is an adaptive method which selects users in a manner which targets their influential neighbors. The advantage of such an approach is that it leverages the friendship paradox in social networks: while users are often not influential, they often know someone who is. Despite the various complexities in such optimization problems, we show that scalable adaptive seeding is achievable. In particular, we develop algorithms for linear influence models with provable approximation guarantees that can be gracefully parallelized. To show the effectiveness of our methods we collected data from various verticals social network users follow. For each vertical, we collected data on the users who responded to a certain post as well as their neighbors, and applied our methods on this data. Our experiments show that adaptive seeding is scalable, and importantly, that it obtains dramatic improvements over standard approaches of information dissemination.Comment: Full version of the paper appearing in WWW 201

On Connections Between Machine Learning And Information Elicitation, Choice Modeling, And Theoretical Computer Science

Machine learning, which has its origins at the intersection of computer science and statistics, is now a rapidly growing area of research that is being integrated into almost every discipline in science and business such as economics, marketing and information retrieval. As a consequence of this integration, it is necessary to understand how machine learning interacts with these disciplines and to understand fundamental questions that arise at the resulting interfaces. The goal of my thesis research is to study these interdisciplinary questions at the interface of machine learning and other disciplines including mechanism design/information elicitation, preference/choice modeling, and theoretical computer science

Delegated Stochastic Probing

Delegation covers a broad class of problems in which a principal doesn\u27t have the resources or expertise necessary to complete a task by themselves, so they delegate the task to an agent whose interests may not be aligned with their own. Stochastic probing describes problems in which we are tasked with maximizing expected utility by "probing" known distributions for acceptable solutions subject to certain constraints. In this work, we combine the concepts of delegation and stochastic probing into a single mechanism design framework which we term delegated stochastic probing. We study how much a principal loses by delegating a stochastic probing problem, compared to their utility in the non-delegated solution. Our model and results are heavily inspired by the work of Kleinberg and Kleinberg in "Delegated Search Approximates Efficient Search." Building on their work, we show that there exists a connection between delegated stochastic probing and generalized prophet inequalities, which provides us with constant-factor deterministic mechanisms for a large class of delegated stochastic probing problems. We also explore randomized mechanisms in a simple delegated probing setting, and show that they outperform deterministic mechanisms in some instances but not in the worst case