We present an early investigation into the use of neural diffusion processes for global optimisation, focusing on Zhang et al.'s Path Integral Sampler. One can use the Boltzmann distribution to formulate optimization as solving a Schr odinger bridge sampling problem, then apply Girsanov's theorem with a simple (single-point) prior to frame it in stochastic control terms, and compute the solution's integral terms via a neural approximation (a Fourier MLP). We provide theoretical bounds for this optimiser, results on toy optimisation tasks, and a summary of the stochastic theory motivating the model. Ultimately, we found the optimiser to display promising per-step performance at optimisation tasks between 2 and 1,247 dimensions, but struggle to explore higher-dimensional spaces when faced with a 15.9k parameter model, indicating a need for work on adaptation in such environments.

We propose a novel strategy for training neural networks using se(cid:173) quential sampling-importance resampling algorithms. This global optimisation strategy allows us to learn the probability distribu(cid:173) tion of the network weights in a sequential framework. It is well suited to applications involving on-line, nonlinear, non-Gaussian or non-stationary signal processing.

Optimising black-box functions is important in many disciplines, such as tuning machine learning models, robotics, finance and mining exploration. Bayesian optimisation is a state-of-the-art technique for the global optimisation of black-box functions which are expensive to evaluate. At the core of this approach is a Gaussian process prior that captures our belief about the distribution over functions. However, in many cases a single Gaussian process is not flexible enough to capture non-stationarity in the objective function. Consequently, heteroscedasticity negatively affects performance of traditional Bayesian methods. In this paper, we propose a novel prior model with hierarchical parameter learning that tackles the problem of non-stationarity in Bayesian optimisation. Our results demonstrate substantial improvements in a wide range of applications, including automatic machine learning and mining exploration.

We propose a novel strategy for training neural networks using sequential sampling-importance resampling algorithms. This global optimisation strategy allows us to learn the probability distribution of the network weights in a sequential framework. It is well suited to applications involving online, nonlinear, non-Gaussian or non-stationary signal processing. 1 INTRODUCTION This paper addresses sequential training of neural networks using powerful sampling techniques. Sequential techniques are important in many applications of neural networks involving real-time signal processing, where data arrival is inherently sequential. Furthermore, one might wish to adopt a sequential training strategy to deal with non-stationarity in signals, so that information from the recent past is lent more credence than information from the distant past. One way to sequentially estimate neural network models is to use a state space formulation and the extended Kalman filter (Singhal and Wu 1988, de Freitas, Niranjan and Gee 1998).

We propose a novel strategy for training neural networks using sequential sampling-importance resampling algorithms. This global optimisation strategy allows us to learn the probability distribution of the network weights in a sequential framework. It is well suited to applications involving online, nonlinear, non-Gaussian or non-stationary signal processing. 1 INTRODUCTION This paper addresses sequential training of neural networks using powerful sampling techniques. Sequential techniques are important in many applications of neural networks involving real-time signal processing, where data arrival is inherently sequential. Furthermore, one might wish to adopt a sequential training strategy to deal with non-stationarity in signals, so that information from the recent past is lent more credence than information from the distant past. One way to sequentially estimate neural network models is to use a state space formulation and the extended Kalman filter (Singhal and Wu 1988, de Freitas, Niranjan and Gee 1998).