Approximate Modularity Revisited

Speaker: Inbal Talgam-Cohen , Hebrew University

Date: Thursday, April 20, 2017

Time: 4:00 PM to 5:00 PM Note: all times are in the Eastern Time Zone

Public: Yes

Location: Seminar Room G575

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Host: Pritish Kamath and Akshay Degwekar

Contact: Akshay Dhananjai Degwekar,

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Reminder Subject: TALK: Approximate Modularity Revisited

Set functions with convenient properties (such as submodularity) often arise in algorithmic game theory, and allow for improved properties of optimization algorithms and mechanisms. It is natural to ask (e.g., in the context of data driven applications) how robust such properties are, and whether small deviations from them can be tolerated. We consider two such questions in the important special case of linear set functions. One question that we address is whether any set function that approximately satisfies the modularity equation (linear functions satisfy the modularity equation exactly) is close to a linear function. The answer to this is positive (in a precise formal sense) as shown by Kalton and Roberts [1983] (and further improved by Bondarenko, Prymak, and Radchenko [2013]). We revisit their proof idea that is based on expander graphs, and provide significantly stronger upper bounds by combining it with new techniques. Furthermore, we provide improved lower bounds for this problem. Another question that we address is that of how to learn a linear function $h$ that is close to an approximately linear function $f$, while querying the value of $f$ on only a small number of sets.

Joint work with Uriel Feige and Michal Feldman.

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See other events that are part of the Algorithms and Complexity Seminar Series 2016/2017.

Created by Akshay Dhananjai Degwekar Email at Monday, April 17, 2017 at 6:35 PM.