Despite recent innovations in network architectures and loss functions, training RNNs to learn long-term dependencies remains difficult due to challenges with gradient-based optimisation methods. Inspired by the success of Deep Neuroevolution in reinforcement learning (Such et al. 2017), we explore the use of gradient-free population-based global optimisation (PBO) techniques -- training RNNs to capture long-term dependencies in time-series data. Testing evolution strategies (ES) and particle swarm optimisation (PSO) on an application in volatility forecasting, we demonstrate that PBO methods lead to performance improvements in general, with ES exhibiting the most consistent results across a variety of architectures.
In March 2017, OpenAI released a blog post on evolution strategies, an optimisation technique that has been around for several decades. The novelty of their paper was that they managed to apply the technique to deep neural networks in the context of reinforcement learning (RL) problems. Before this, the optimisation of deep learning RL models (with typically millions of parameters) was typically achieved with backpropagation. Using evolution strategies for deep neural network (DNN) optimisation seemingly unlocked an exciting new toolbox for deep learning researchers to play with.
Computational techniques have shown much promise in the field of Finance, owing to their ability to extract sense out of dauntingly complex systems. This paper reviews the most promising of these techniques, from traditional computational intelligence methods to their machine learning siblings, with particular view to their application in optimising the management of a portfolio of financial instruments. The current state of the art is assessed, and prospective further work is assessed and recommended
Bayesian optimisation is an important decision-making tool for high-stakes applications in drug discovery and materials design. An oft-overlooked modelling consideration however is the representation of input-dependent or heteroscedastic aleatoric uncertainty. The cost of misrepresenting this uncertainty as being homoscedastic could be high in drug discovery applications where neglecting heteroscedasticity in high throughput virtual screening could lead to a failed drug discovery program. In this paper, we propose a heteroscedastic Bayesian optimisation scheme which both represents and penalises aleatoric noise in the suggestions.Our scheme features a heteroscedastic Gaussian Process (GP) as the surrogate model in conjunction with two acquisition heuristics. First, we extend the augmented expected improvement (AEI) heuristic to the heteroscedastic setting and second, we introduce a new acquisition function, aleatoric-penalised expected improvement (ANPEI) based on a simple scalarisation of the performance and noise objective. Both methods penalise aleatoric noise in the suggestions and yield improved performance relative to a naive implementation of homoscedastic Bayesian optimisation on toy problems as well as a real-world optimisation problem.
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.