On the construction of probabilistic Newton-type algorithms
This work addresses optimization in noisy, real-world scenarios like system identification, but it is incremental as it builds on existing quasi-Newton and probabilistic methods.
The authors tackled the problem of stochastic optimization where only noisy observations of the cost function and its derivatives are available, by developing a probabilistic quasi-Newton algorithm that unites Gaussian process models with probabilistic line search, showing promising results on challenging nonlinear system identification problems.
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.