Optimal decision making under uncertainty is critical for efficient control and optimization

of complex systems. However, many current techniques encounter the curse-of-dimensionality

for systems with too many state variables. In this talk, we will present a framework based on the

emerging area of tensor decompositions that mitigates this curse-of-dimensionality. First we de-

scribe the tensor-train decomposition, which provides efficient compression of high dimensional

arrays. Next, we describe our recent work utilizing the tensor-train decomposition for optimal

stochastic control, and we simulate the resulting optimal feedback control on an underactuated

motion planning problem. In the second part of the talk, we will describe the construction of

our newly developed continuous extension to the tensor-train decomposition. The resulting ap-

proximation, termed the function-train, is obtained using an algorithm designed in the spirit of

continuous computation. It involves computing “continuous” matrix-factorizations such as the

LU and QR decomposition of univariate functions. Finally, we will show how this new approx-

imation can be used to integrate high dimensional and discontinuous functions in polynomial

time with dimension . We will also show its approximation properties on a parameteric elliptic

PDE.

# Exploiting low-rank structure in optimal stochastic control and function approximation

30 October 2015

12:00 pm

Exploiting low-rank structure in optimal stochastic control and function approximation

Alex Gorodetsky

PhD Candidate

Aerospace Computational Design Laboratory

Department of Aeronautics and Astronautics

MIT