UNIVERSAL HALTING TIMES IN OPTIMIZATION AND MACHINE LEARNING

We present empirical evidence that the halting times for a class of optimization algorithms are universal. The algorithms we consider come from quadratic optimization, spin glasses and machine learning. A universality theorem is given in the case of the quadratic gradient descent flow. More precisely, given an algorithm, which we take to be both the optimization routine and the form of the random landscape, the fluctuations of the halting time of the algorithm follow a distribution that, after centering and scaling, appears invariant under changes in the distribution on the landscape universality is present.