26,370 research outputs found
On the construction of probabilistic Newton-type algorithms
It has recently been shown that many of the existing quasi-Newton algorithms
can be formulated as learning algorithms, capable of learning local models of
the cost functions. Importantly, this understanding allows us to safely start
assembling probabilistic Newton-type algorithms, applicable in situations where
we only have access to noisy observations of the cost function and its
derivatives. This is where our interest lies.
We make contributions to the use of the non-parametric and probabilistic
Gaussian process models in solving these stochastic optimisation problems.
Specifically, we present a new algorithm that unites these approximations
together with recent probabilistic line search routines to deliver a
probabilistic quasi-Newton approach.
We also show that the probabilistic optimisation algorithms deliver promising
results on challenging nonlinear system identification problems where the very
nature of the problem is such that we can only access the cost function and its
derivative via noisy observations, since there are no closed-form expressions
available
A Simple and Efficient Algorithm for Nonlinear Model Predictive Control
We present PANOC, a new algorithm for solving optimal control problems
arising in nonlinear model predictive control (NMPC). A usual approach to this
type of problems is sequential quadratic programming (SQP), which requires the
solution of a quadratic program at every iteration and, consequently, inner
iterative procedures. As a result, when the problem is ill-conditioned or the
prediction horizon is large, each outer iteration becomes computationally very
expensive. We propose a line-search algorithm that combines forward-backward
iterations (FB) and Newton-type steps over the recently introduced
forward-backward envelope (FBE), a continuous, real-valued, exact merit
function for the original problem. The curvature information of Newton-type
methods enables asymptotic superlinear rates under mild assumptions at the
limit point, and the proposed algorithm is based on very simple operations:
access to first-order information of the cost and dynamics and low-cost direct
linear algebra. No inner iterative procedure nor Hessian evaluation is
required, making our approach computationally simpler than SQP methods. The
low-memory requirements and simple implementation make our method particularly
suited for embedded NMPC applications
Second order gradient ascent pulse engineering
We report some improvements to the gradient ascent pulse engineering (GRAPE)
algorithm for optimal control of quantum systems. These include more accurate
gradients, convergence acceleration using the BFGS quasi-Newton algorithm as
well as faster control derivative calculation algorithms. In all test systems,
the wall clock time and the convergence rates show a considerable improvement
over the approximate gradient ascent.Comment: Submitted for publicatio
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