The Dominant Eigenvalue of an Essentially Nonnegative Tensor

It is well known that the dominant eigenvalue of a real essentially nonnegative matrix is a convex function of its diagonal entries. This convexity is of practical importance in population biology, graph theory, demography, analytic hierarchy process and so on. In this paper, the concept of essentially nonnegativity is extended from matrices to higher order tensors, and the convexity and log convexity of dominant eigenvalues for such a class of tensors are established. Particularly, for any nonnegative tensor, the spectral radius turns out to be the dominant eigenvalue and hence possesses these convexities. Finally, an algorithm is given to calculate the dominant eigenvalue, and numerical results are reported to show the effectiveness of the proposed algorithm

Virtual to Real Reinforcement Learning for Autonomous Driving

Reinforcement learning is considered as a promising direction for driving policy learning. However, training autonomous driving vehicle with reinforcement learning in real environment involves non-affordable trial-and-error. It is more desirable to first train in a virtual environment and then transfer to the real environment. In this paper, we propose a novel realistic translation network to make model trained in virtual environment be workable in real world. The proposed network can convert non-realistic virtual image input into a realistic one with similar scene structure. Given realistic frames as input, driving policy trained by reinforcement learning can nicely adapt to real world driving. Experiments show that our proposed virtual to real (VR) reinforcement learning (RL) works pretty well. To our knowledge, this is the first successful case of driving policy trained by reinforcement learning that can adapt to real world driving data