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Optimal approximation for unconstrained non-submodular minimization
Marwa El Halabi · Stefanie Jegelka

Wed Jul 15 05:00 AM -- 05:45 AM & Wed Jul 15 07:00 PM -- 07:45 PM (PDT) @ Virtual #None

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function is not exactly submodular, but close. In this case, no theoretical guarantees exist. Indeed, submodular minimization algorithms rely on intricate connections between submodularity and convexity. We show how these relations can be extended to obtain approximation guarantees for minimizing non-submodular functions, characterized by how close the function is to submodular. We also extend this result to noisy function evaluations. Our approximation results are the first for minimizing non-submodular functions, and are optimal, as established by our matching lower bound.

Author Information

Marwa El Halabi (MIT)
Stefanie Jegelka (Massachusetts Institute of Technology)

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