Default policies for global optimisation of noisy functions with severe noise

Global optimisation of unknown noisy functions is a daunting task that appears in domains ranging from games to control problems to meta-parameter optimisation for machine learning. We show how to incorporate heuristics to Stochastic Simultaneous Optimistic Optimization (STOSOO), a global optimisation algorithm that has very weak requirements from the function. In our case, heuristics come in the form of Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The new algorithm, termed Guided STOSOO (STOSOO-G), combines the ability of CMA-ES for fast local convergence (due to the algorithm following the “natural” gradient) and the global optimisation abilities of STOSOO. We compare all three algorithms in the “harder” parts of the Comparing Continuous Optimisers on Black-Box Optimization Benchmarking benchmark suite, which provides a default set of functions for testing. We show that our approach keeps the best of both worlds, i.e. the almost optimal exploration/exploitation of STOSOO with the local optimisation strength of CMA-ES

Implications of the financial crisis for models in monetary policy

Monetary authorities have been implicated in the financial crisis of 2007-2008. John Muellbauer, for example, has blamed what he thought was initially inadequate policy responses by central banks to the crisis on their models, which are, in his words, “overdue for the scrap heap”. This paper investigates the role of monetary policy models in the crisis and finds that (i) it is likely that monetary policy contributed to the financial crisis and (ii) that an inappropriately narrow suite of models made this mistake easier. The core models currently used at prominent central banks were not designed to discover emergent financial fragility. In that respect John Muellbauer is right. But the implications drawn here are less dramatic than his: while the representative agent approach to microfoundations now seems indefensible, other aspects of modern macroeconomics are not similarly suspect. The case made here is rather for expanding the suite of models used in the regular deliberations of monetary authorities, with new models that give explicit roles to the financial sector, to money and to the process of exchange. Recommending a suite of models for policy making entails no methodological innovation. That is what central banks do; though, of course, how they do it is open to improvement. The methodological innovation is the inclusion of a model that would be sensitive to financial fragility, a sensitivity that was absent in the run-up to the current financial crisis.Monetary policy, financial crisis, methodology of policy models

Bayesian optimisation of restriction zones for bluetongue control.

We investigate the restriction of animal movements as a method to control the spread of bluetongue, an infectious disease of livestock that is becoming increasingly prevalent due to the onset of climate change. We derive control policies for the UK that minimise the number of infected farms during an outbreak using Bayesian optimisation and a simulation-based model of BT. Two cases are presented: first, where the region of introduction is randomly selected from England and Wales to find a generalised strategy. This "national" model is shown to be just as effective at subduing the spread of bluetongue as the current strategy of the UK government. Our proposed controls are simpler to implement, affect fewer farms in the process and, in so doing, minimise the potential economic implications. Second, we consider policies that are tailored to the specific region in which the first infection was detected. Seven different regions in the UK were explored and improvements in efficiency from the use of specialised policies presented. As a consequence of the increasing temperatures associated with climate change, efficient control measures for vector-borne diseases such as this are expected to become increasingly important. Our work demonstrates the potential value of using Bayesian optimisation in developing cost-effective disease management strategies

Towards Deep Learning with Competing Generalisation Objectives

The unreasonable effectiveness of Deep Learning continues to deliver unprecedented Artificial Intelligence capabilities to billions of people. Growing datasets and technological advances keep extending the reach of expressive model architectures trained through efficient optimisations. Thus, deep learning approaches continue to provide increasingly proficient subroutines for, among others, computer vision and natural interaction through speech and text. Due to their scalable learning and inference priors, higher performance is often gained cost-effectively through largely automatic training. As a result, new and improved capabilities empower more people while the costs of access drop. The arising opportunities and challenges have profoundly influenced research. Quality attributes of scalable software became central desiderata of deep learning paradigms, including reusability, efficiency, robustness and safety. Ongoing research into continual, meta- and robust learning aims to maximise such scalability metrics in addition to multiple generalisation criteria, despite possible conflicts. A significant challenge is to satisfy competing criteria automatically and cost-effectively. In this thesis, we introduce a unifying perspective on learning with competing generalisation objectives and make three additional contributions. When autonomous learning through multi-criteria optimisation is impractical, it is reasonable to ask whether knowledge of appropriate trade-offs could make it simultaneously effective and efficient. Informed by explicit trade-offs of interest to particular applications, we developed and evaluated bespoke model architecture priors. We introduced a novel architecture for sim-to-real transfer of robotic control policies by learning progressively to generalise anew. Competing desiderata of continual learning were balanced through disjoint capacity and hierarchical reuse of previously learnt representations. A new state-of-the-art meta-learning approach is then proposed. We showed that meta-trained hypernetworks efficiently store and flexibly reuse knowledge for new generalisation criteria through few-shot gradient-based optimisation. Finally, we characterised empirical trade-offs between the many desiderata of adversarial robustness and demonstrated a novel defensive capability of implicit neural networks to hinder many attacks simultaneously

Bayesian inference for biological time series

Inferring the parameters of time series models from observed data is essential across many areas of science. Bayesian statistics provides a powerful framework for this purpose, but significant challenges arise when time series models are misspecified due to complexities in the underlying process (e.g., heterogeneity in the modelled population, or when parameter values fluctuate over time), inaccurate numerical approximation of the forward model (e.g., in models involving differential equations), or the presence of non-stationary, non-independent error terms. We introduce a series of models and computational strategies for dealing with misspecification in time series inference problems, with a particular focus on time series problems arising in epidemiology and problems involving ordinary differential equations. The models and inference strategies discussed include: 1. A generalisation of the Poisson renewal model to allow heterogeneous behaviour between local and imported cases, which we use to show that accounting for such heterogeneous behaviour is essential for accurate inference of the time-varying reproduction number (Rt); 2. A Bayesian nonparametric approach to flexibly learn time variation in Rt, which we show is capable of learning accurate and precise estimates of the parameter; 3. Estimates of the gradient and the error in the log-likelihood arising from numerical approximation of differential equations derived from a posteriori error analysis; and 4. A flexible noise process accommodating correlated and heteroscedastic error terms and whose form can be inferred from time series data using kernel functions. We motivate our methodological innovation by a comprehensive examination of the biases in inference that result from insufficiently accurate numerical approximation of differential equations, as well as time series inverse problems and models drawn from epidemiology, hydrology, and cardiac electrophysiology

Bayesian optimization in adverse scenarios

Optimization problems with expensive-to-evaluate objective functions are ubiquitous in scientific and industrial settings. Bayesian optimization has gained widespread acclaim for optimizing expensive (and often black box) functions due to its theoretical performance guarantees and empirical sample efficiency in a variety of settings. Nevertheless, many practical scenarios remain where prevailing Bayesian optimization techniques fall short. We consider four such scenarios. First, we formalize the optimization problem where the goal is to identify robust designs with respect to multiple objective functions that are subject to input noise. Such robust design problems frequently arise, for example, in manufacturing settings where fabrication can only be performed with limited precision. We propose a method that identifies a set of optimal robust designs, where each design provides probabilistic guarantees jointly on multiple objectives. Second, we consider sample-efficient high-dimensional multi-objective optimization. This line of research is motivated by the challenging task of designing optical displays for augmented reality to optimize visual quality and efficiency, where the designs are specified by high-dimensional parameterizations governing complex geometries. Our proposed trust-region based algorithm yields order-of-magnitude improvements in sample complexity on this problem. Third, we consider multi-objective optimization of expensive functions with variable-cost, decoupled, and/or multi-fidelity evaluations and propose a Bayes-optimal, non-myopic acquisition function, which significantly improves sample efficiency in scenarios with incomplete information. We apply this to hardware-aware neural architecture search where the objective, on-device latency and model accuracy, can often be evaluated independently. Fourth, we consider the setting where the search space consists of discrete (and potentially continuous) parameters. We propose a theoretically grounded technique that uses a probabilistic reparameterization to transform the discrete or mixed inner optimization problem into a continuous one leading to more effective Bayesian optimization policies. Together, this thesis provides a playbook for Bayesian optimization in several practical adverse scenarios

Computation Approaches for Continuous Reinforcement Learning Problems

Optimisation theory is at the heart of any control process, where we seek to control the behaviour of a system through a set of actions. Linear control problems have been extensively studied, and optimal control laws have been identified. But the world around us is highly non-linear and unpredictable. For these dynamic systems, which don’t possess the nice mathematical properties of the linear counterpart, the classic control theory breaks and other methods have to be employed. But nature thrives by optimising non-linear and over-complicated systems. Evolutionary Computing (EC) methods exploit nature’s way by imitating the evolution process and avoid to solve the control problem analytically. Reinforcement Learning (RL) from the other side regards the optimal control problem as a sequential one. In every discrete time step an action is applied. The transition of the system to a new state is accompanied by a sole numerical value, the “reward” that designate the quality of the control action. Even though the amount of feedback information is limited into a sole real number, the introduction of the Temporal Difference method made possible to have accurate predictions of the value-functions. This paved the way to optimise complex structures, like the Neural Networks, which are used to approximate the value functions. In this thesis we investigate the solution of continuous Reinforcement Learning control problems by EC methodologies. The accumulated reward of such problems throughout an episode suffices as information to formulate the required measure, fitness, in order to optimise a population of candidate solutions. Especially, we explore the limits of applicability of a specific branch of EC, that of Genetic Programming (GP). The evolving population in the GP case is comprised from individuals, which are immediately translated to mathematical functions, which can serve as a control law. The major contribution of this thesis is the proposed unification of these disparate Artificial Intelligence paradigms. The provided information from the systems are exploited by a step by step basis from the RL part of the proposed scheme and by an episodic basis from GP. This makes possible to augment the function set of the GP scheme with adaptable Neural Networks. In the quest to achieve stable behaviour of the RL part of the system a modification of the Actor-Critic algorithm has been implemented. Finally we successfully apply the GP method in multi-action control problems extending the spectrum of the problems that this method has been proved to solve. Also we investigated the capability of GP in relation to problems from the food industry. These type of problems exhibit also non-linearity and there is no definite model describing its behaviour