Grothendieck inequality and hyperbolicity (Sebastien Bubeck)

Let me warn you that this open problem is more open ended than the one on Thompson Sampling!

Grothendieck’s inequality and its proof by Gaussian projection give a universal rounding scheme for semidefinite programs. The question is whether there exist a generalization of Grothendieck’s inequality to hyperbolic programs, and what would the rounding scheme look like in this case?

Some readings:

– See section 7 here for a clean description of hyperbolic programming and the associated basic concepts.

– See section 2 here for a simple proof of Grothendieck’s inequality.

– Known connections between hyperbolicity and probability will probably be useful here, see this survey by Robin Pemantle.

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