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Submodular Optimization: From Discrete to Continuous and Back

Hamed Hassani · Amin Karbasi


This tutorial will cover recent advancements in discrete optimization methods prevalent in large-scale machine learning problems. Traditionally, machine learning has been harnessing convex optimization to design fast algorithms with provable guarantees for a broad range of applications. In recent years, however, there has been a surge of interest in applications that involve discrete optimization. For discrete domains, the analog of convexity is considered to be submodularity, and the evolving theory of submodular optimization has been a catalyst for progress in extraordinarily varied application areas including active learning and experimental design, vision, sparse reconstruction, graph inference, video analysis, clustering, document summarization, object detection, information retrieval, network inference, interpreting neural network, and discrete adversarial attacks.

As applications and techniques of submodular optimization mature, a fundamental gap between theory and application emerges. In the past decade, paradigms such as large-scale learning, distributed systems, and sequential decision making have enabled a quantum leap in the performance of learning methodologies. Incorporating these paradigms in discrete problems has led to fundamentally new frameworks for submodular optimization. The goal of this tutorial is to cover rigorous and scalable foundations for discrete optimization in complex, dynamic environments, addressing challenges of scalability and uncertainty, and facilitating distributed and sequential learning in broader discrete settings.

Here is the website for the tutorial that contains further details as well as the slides:

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