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Creators/Authors contains: "Bhojanapalli, Srinadh"

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  1. ; ; ; ; ; (, International Conference on Learning Representations (ICLR))
    Accepted Manuscript Full Text Available
  2. ; ; ; ; (, International Conference on Learning Representations (ICLR))
    Accepted Manuscript Full Text Available
  3. ; ; ; (, Proceedings of the 31st Conference On Learning Theory, PMLR)
    Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer–Monteiro factorization approach for solving SDPs. For a large class of SDPs, upon random perturbation of the cost matrix, with high probability, we show that all approximate second-order stationary points are approximate global optima for the penalty formulation of appropriately rank-constrained SDPs, as long as the number of constraints scales sub-quadratically with the desired rank. Our result is based on a simple penalty function formulation of the rank-constrained SDP along with a smoothed analysis to avoid worst-case cost matrices. We particularize our results to two applications, namely, Max-Cut and matrix completion. 
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    Accepted Manuscript Full Text Available
  4. ; ; ; ; (, arXiv.org)
    We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix X with gradient descent on a factorization of X. We conjecture and provide empirical and theoretical evidence that with small enough step sizes and initialization close enough to the origin, gradient descent on a full dimensional factorization converges to the minimum nuclear norm solution. 
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    Accepted Manuscript Full Text Available
  5. ; ; (, arXiv.org)
    We show that there are no spurious local minima in the non-convex factorized parametrization of low-rank matrix recovery from incoherent linear measurements. With noisy measurements we show all local minima are very close to a global optimum. Together with a curvature bound at saddle points, this yields a polynomial time global convergence guarantee for stochastic gradient descent from random initialization. 
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    Accepted Manuscript Full Text Available