We make three contributions toward better understanding policy gradient methods in the
tabular setting. First, we show that with the true gradient, policy gradient with a softmax …

Optimization algorithms can see their local convergence rates deteriorate when the Hessian
at the optimum is singular. These singularities are inescapable when the optima are non …

Do you know the difference between an optimist and a pessimist? The former believes we
live in the best possible world, and the latter is afraid that the former might be right.… In that …

Stochastic gradient descent (SGD) has been found to be surprisingly effective in training a
variety of deep neural networks. However, there is still a lack of understanding on how and …

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of
functions satisfying gradient dominance property with $1\le\alpha\le2 $ which holds in a …

The gradient descent-ascent (GDA) algorithm has been widely applied to solve minimax
optimization problems. In order to achieve convergent policy parameters for minimax …

Cubic regularization (CR) is an optimization method with emerging popularity due to its
capability to escape saddle points and converge to second-order stationary solutions for …

Many important machine learning applications involve regularized nonconvex bi-level
optimization. However, the existing gradient-based bi-level optimization algorithms cannot …

Momentum is a popular technique to accelerate the convergence in practical training, and its
impact on convergence guarantee has been well-studied for first-order algorithms. However …

Trust-region methods (TR) can converge quadratically to minima where the Hessian is
positive definite. However, if the minima are not isolated, then the Hessian there cannot be …