Gaussian, to an unknown data distribution, which is only represented by empirical samples. In order to measure the mapping quality, various metrics between the probability distributions have been proposed.

Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare.

We study gradient-based optimization methods obtained by directly discretizing a second-order ordinary differential equation (ODE) related to the continuous limit of Nesterov's accelerated gradient method. When the function is smooth enough, we show that acceleration can be achieved by a stable discretization of this ODE using standard Runge-Kutta integrators.

To this end, we use algorithms developed in the gradient-based multi-objective optimization literature. These algorithms are not directly applicable to large-scale learning problems since they scale poorly with the dimensionality of the gradients and the number of tasks. We therefore propose an upper bound for the multi-objective loss and show that it can be optimized efficiently. We further prove that optimizing this upper bound yields a Pareto optimal solution under realistic assumptions.

Bayesian optimization usually assumes that a Bayesian prior is given.

Neural Information Processing Systems http://nips.cc/

We extend the recent framework of Osokin et al.

Neural Information Processing Systems http://nips.cc/

We study a safe reinforcement learning problem in which the constraints are defined as the expected cost over finite-length trajectories.