Abstract: The Gaussian process (GP) has over the past 5-7 years become a standard tool within system identification. One important starting point was the successful use of the GP in estimating the impulse response of a linear system. Since then the GP has also been used to construct non-parametric nonlinear state-space models and for on-line nonlinear black-box modelling, etc. In this talk I will focus on one of our recent developments where we show how the GP can be used to solve stochastic optimization problems. These problems have been studied for a long time and due to the success of deep learning these problems are now more relevant than ever. Our main motivation in this talk comes from another problem though, namely the problem of nonlinear system identification. Here, 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. Via sequential Mote Carlo methods (aka particle filters) we can obtain unbiased estimates of the likelihood function. We start from the fact that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Inspired by this we can start assembling stochastic 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 will show how we can make use of the GP model to learn the Hessian allowing for efficient solution of these stochastic optimisation problems. I will also mention some ongoing work where we scale this to much higher dimensions (in terms of the size of the dataset and the number of unknown parameters). If there is time towards the end I will also show a few additional GP constructions that we have been developing recently.

Slides

Abstract:

Enabling an embodied agent to act autonomously in the physical world is one of the long-standing challenges of artificial intelligence. Besides its practical implications it is also an interesting testbed for generallearning algorithms.

Abstract: Though seemingly very different, randomised optimisation and statistical learning theory in fact enjoy deep connections. One of these relies on the notion of compression. This is the observation that under some conditions, when using a large data sample to make decisions (learn a "concept" in machine learning, or minimise a cost function subject to constraints in optimisation), the final decision we come to will generally only depend on a small sub-sample of fixed cardinality. The effect of the remaining samples is only to provide confidence; the more samples we have seen the more confident we are that the decision we made is good. The talk will introduce the compression notion using learning of concepts in statistical learning theory. We will then explore its implications for decision making under uncertainty based on scenario optimisation.

Slides