ML Reading Group - Quantum gradient descent

This is a university style reading group where we have a round table discussion of an interesting paper.

For this months paper we will read about a quantum variant of gradient descent.

Paper:

Quantum gradient descent and Newton's method for constrained polynomial optimization

https://scirate.com/arxiv/1612.01789

Abstract:
Solving optimization problems in disciplines such as machine learning is commonly done by iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into account curvature information and thereby often improves convergence. Here, we develop quantum versions of these iterative optimization algorithms and apply them to homogeneous polynomial optimization with a unit norm constraint. In each step, multiple copies of the current candidate are used to improve the candidate using quantum phase estimation, an adapted quantum principal component analysis scheme, as well as quantum matrix multiplications and inversions. The required operations perform polylogarithmically in the dimension of the solution vector, an exponential speed-up over classical algorithms, which scale polynomially. The quantum algorithm can therefore be beneficial for high dimensional problems where a relatively small number of iterations is sufficient.

Please have at least have a glance at the paper before the event! Thanks.