Substantial progress has been made recently on develo** provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in
the high-dimensional regime. We prove limit theorems for the trajectories of summary …

Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …

This paper considers the problem of solving systems of quadratic equations, namely,
recovering an object of interest x^ ♮ ∈ R^ nx♮∈ R n from m quadratic equations/samples …

We study derivative-free methods for policy optimization over the class of linear policies. We
focus on characterizing the convergence rate of these methods when applied to linear …

Many modern learning tasks involve fitting nonlinear models which are trained in an
overparameterized regime where the parameters of the model exceed the size of the …

Phase retrieval, ie the problem of recovering a function from the squared magnitude of its
Fourier transform, arises in many applications, such as X-ray crystallography, diffraction …

Despite the non-convex optimization landscape, over-parametrized shallow networks are
able to achieve global convergence under gradient descent. The picture can be radically …

We study the problem of solving a quadratic system of equations, ie, recovering a vector
signal x ε R n from its magnitude measurements yi=|〈 ai, x〉|, i= 1,..., m. We develop a …