arXiv subjects

Michael A. Osborne

Publications and source records attributed to Michael A. Osborne.

At least 55 records · Page 3Linked to original sources

arXiv2019

Adaptive Configuration Oracle for Online Portfolio Selection Methods

Financial markets are complex environments that produce enormous amounts of noisy and non-stationary data. One fundamental problem is online portfolio selection, the goal of which is to exploit this data to sequentially select portfolios of assets to achieve positive investment outcomes while managing risks. Various algorithms have been proposed for solving this problem in fields such as finance, statistics and machine learning, among others. Most of the methods have parameters that are estimated from backtests for good performance. Since these algorithms operate on non-stationary data that reflects the complexity of financial markets, we posit that adaptively tuning these parameters in an intelligent manner is a remedy for dealing with this complexity. In this paper, we model the mapping between the parameter space and the space of performance metrics using a Gaussian process prior. We then propose an oracle based on adaptive Bayesian optimization for automatically and adaptively configuring online portfolio selection methods. We test the efficacy of our solution on algorithms operating on equity and index data from various markets.

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arXiv2019

Asynchronous Batch Bayesian Optimisation with Improved Local Penalisation

Batch Bayesian optimisation (BO) has been successfully applied to hyperparameter tuning using parallel computing, but it is wasteful of resources: workers that complete jobs ahead of others are left idle. We address this problem by developing an approach, Penalising Locally for Asynchronous Bayesian Optimisation on $k$ workers (PLAyBOOK), for asynchronous parallel BO. We demonstrate empirically the efficacy of PLAyBOOK and its variants on synthetic tasks and a real-world problem. We undertake a comparison between synchronous and asynchronous BO, and show that asynchronous BO often outperforms synchronous batch BO in both wall-clock time and number of function evaluations.

stat.ML↗

arXiv2019

Fingerprint Policy Optimisation for Robust Reinforcement Learning

Policy gradient methods ignore the potential value of adjusting environment variables: unobservable state features that are randomly determined by the environment in a physical setting, but are controllable in a simulator. This can lead to slow learning, or convergence to suboptimal policies, if the environment variable has a large impact on the transition dynamics. In this paper, we present fingerprint policy optimisation (FPO), which finds a policy that is optimal in expectation across the distribution of environment variables. The central idea is to use Bayesian optimisation (BO) to actively select the distribution of the environment variable that maximises the improvement generated by each iteration of the policy gradient method. To make this BO practical, we contribute two easy-to-compute low-dimensional fingerprints of the current policy. Our experiments show that FPO can efficiently learn policies that are robust to significant rare events, which are unlikely to be observable under random sampling, but are key to learning good policies.

cs.LG↗

arXiv2019

Automated Model Selection with Bayesian Quadrature

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for computationally expensive models. Previous research has shown that BQ offers sample efficiency superior to Monte Carlo in computing the evidence of an individual model. However, applying BQ directly to model comparison may waste computation producing an overly-accurate estimate for the evidence of a clearly poor model. We propose an automated and efficient algorithm for computing the most-relevant quantity for model selection: the posterior probability of a model. Our technique maximizes the mutual information between this quantity and observations of the models' likelihoods, yielding efficient acquisition of samples across disparate model spaces when likelihood observations are limited. Our method produces more-accurate model posterior estimates using fewer model likelihood evaluations than standard Bayesian quadrature and Monte Carlo estimators, as we demonstrate on synthetic and real-world examples.

cs.LG↗

arXiv2018

Rejoinder for "Probabilistic Integration: A Role in Statistical Computation?"

This article is the rejoinder for the paper "Probabilistic Integration: A Role in Statistical Computation?" to appear in Statistical Science with discussion. We would first like to thank the reviewers and many of our colleagues who helped shape this paper, the editor for selecting our paper for discussion, and of course all of the discussants for their thoughtful, insightful and constructive comments. In this rejoinder, we respond to some of the points raised by the discussants and comment further on the fundamental questions underlying the paper: (i) Should Bayesian ideas be used in numerical analysis?, and (ii) If so, what role should such approaches have in statistical computation?

stat.CO↗

arXiv2018

Battery health prediction under generalized conditions using a Gaussian process transition model

Accurately predicting the future health of batteries is necessary to ensure reliable operation, minimise maintenance costs, and calculate the value of energy storage investments. The complex nature of degradation renders data-driven approaches a promising alternative to mechanistic modelling. This study predicts the changes in battery capacity over time using a Bayesian non-parametric approach based on Gaussian process regression. These changes can be integrated against an arbitrary input sequence to predict capacity fade in a variety of usage scenarios, forming a generalised health model. The approach naturally incorporates varying current, voltage and temperature inputs, crucial for enabling real world application. A key innovation is the feature selection step, where arbitrary length current, voltage and temperature measurement vectors are mapped to fixed size feature vectors, enabling them to be efficiently used as exogenous variables. The approach is demonstrated on the open-source NASA Randomised Battery Usage Dataset, with data of 26 cells aged under randomized operational conditions. Using half of the cells for training, and half for validation, the method is shown to accurately predict non-linear capacity fade, with a best case normalised root mean square error of 4.3%, including accurate estimation of prediction uncertainty.

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arXiv2018

Fast Information-theoretic Bayesian Optimisation

Information-theoretic Bayesian optimisation techniques have demonstrated state-of-the-art performance in tackling important global optimisation problems. However, current information-theoretic approaches require many approximations in implementation, introduce often-prohibitive computational overhead and limit the choice of kernels available to model the objective. We develop a fast information-theoretic Bayesian Optimisation method, FITBO, that avoids the need for sampling the global minimiser, thus significantly reducing computational overhead. Moreover, in comparison with existing approaches, our method faces fewer constraints on kernel choice and enjoys the merits of dealing with the output space. We demonstrate empirically that FITBO inherits the performance associated with information-theoretic Bayesian optimisation, while being even faster than simpler Bayesian optimisation approaches, such as Expected Improvement.

stat.ML↗

arXiv2018

Optimization, fast and slow: optimally switching between local and Bayesian optimization

We develop the first Bayesian Optimization algorithm, BLOSSOM, which selects between multiple alternative acquisition functions and traditional local optimization at each step. This is combined with a novel stopping condition based on expected regret. This pairing allows us to obtain the best characteristics of both local and Bayesian optimization, making efficient use of function evaluations while yielding superior convergence to the global minimum on a selection of optimization problems, and also halting optimization once a principled and intuitive stopping condition has been fulfilled.

stat.ML↗

arXiv2018

Practical Bayesian Optimization for Variable Cost Objectives

We propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to sampling support points, allowing faster construction of the acquisition function. This allows us to achieve optimization with lower overheads than previous approaches and is implemented for a more general class of problem. We show this approach to be effective on synthetic and real world benchmark problems.

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arXiv2018

Distributionally Ambiguous Optimization Techniques for Batch Bayesian Optimization

We propose a novel, theoretically-grounded, acquisition function for Batch Bayesian optimization informed by insights from distributionally ambiguous optimization. Our acquisition function is a lower bound on the well-known Expected Improvement function, which requires evaluation of a Gaussian Expectation over a multivariate piecewise affine function. Our bound is computed instead by evaluating the best-case expectation over all probability distributions consistent with the same mean and variance as the original Gaussian distribution. Unlike alternative approaches, including Expected Improvement, our proposed acquisition function avoids multi-dimensional integrations entirely, and can be computed exactly - even on large batch sizes - as the solution of a tractable convex optimization problem. Our suggested acquisition function can also be optimized efficiently, since first and second derivative information can be calculated inexpensively as by-products of the acquisition function calculation itself. We derive various novel theorems that ground our work theoretically and we demonstrate superior performance via simple motivating examples, benchmark functions and real-world problems.

stat.ML↗

arXiv2018

Quantum algorithms for training Gaussian Processes

Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core of which amounts to evaluating the logarithm of the marginal likelihood (LML) of a given model. LML gives a concrete measure of the quality of prediction that a GP model is expected to achieve. The classical computation of LML typically carries a polynomial time overhead with respect to the input size. We propose a quantum algorithm that computes the logarithm of the determinant of a Hermitian matrix, which runs in logarithmic time for sparse matrices. This is applied in conjunction with a variant of the quantum linear system algorithm that allows for logarithmic time computation of the form $\mathbf{y}^TA^{-1}\mathbf{y}$, where $\mathbf{y}$ is a dense vector and $A$ is the covariance matrix. We hence show that quantum computing can be used to estimate the LML of a GP with exponentially improved efficiency under certain conditions.

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arXiv2018

Bayesian Optimization for Dynamic Problems

We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our extensions to Bayesian optimization use the information learnt from this model to guide the tracking of a temporally evolving minimum. By exploiting temporal correlations, the proposed method also determines when to make evaluations, how fast to make those evaluations, and it induces an appropriate budget of steps based on the available information. Lastly, we evaluate our technique on synthetic and real-world problems.

stat.ML↗

arXiv2018

Spatial Field Reconstruction and Sensor Selection in Heterogeneous Sensor Networks with Stochastic Energy Harvesting

We address the two fundamental problems of spatial field reconstruction and sensor selection in het- erogeneous sensor networks. We consider the case where two types of sensors are deployed: the first consists of expensive, high quality sensors; and the second, of cheap low quality sensors, which are activated only if the intensity of the spatial field exceeds a pre-defined activation threshold (eg. wind sensors). In addition, these sensors are powered by means of energy harvesting and their time varying energy status impacts on the accuracy of the measurement that may be obtained. We account for this phenomenon by encoding the energy harvesting process into the second moment properties of the additive noise, resulting in a spatial heteroscedastic process. We then address the following two important problems: (i) how to efficiently perform spatial field reconstruction based on measurements obtained simultaneously from both networks; and (ii) how to perform query based sensor set selection with predictive MSE performance guarantee. We first show that the resulting predictive posterior distribution, which is key in fusing such disparate observations, involves solving intractable integrals. To overcome this problem, we solve the first problem by developing a low complexity algorithm based on the spatial best linear unbiased estimator (S-BLUE). Next, building on the S-BLUE, we address the second problem, and develop an efficient algorithm for query based sensor set selection with performance guarantee. Our algorithm is based on the Cross Entropy method which solves the combinatorial optimization problem in an efficient manner. We present a comprehensive study of the performance gain that can be obtained by augmenting the high-quality sensors with low-quality sensors using both synthetic and real insurance storm surge database known as the Extreme Wind Storms Catalogue.

eess.SP↗

arXiv2017

Alternating Optimisation and Quadrature for Robust Control

Bayesian optimisation has been successfully applied to a variety of reinforcement learning problems. However, the traditional approach for learning optimal policies in simulators does not utilise the opportunity to improve learning by adjusting certain environment variables: state features that are unobservable and randomly determined by the environment in a physical setting but are controllable in a simulator. This paper considers the problem of finding a robust policy while taking into account the impact of environment variables. We present Alternating Optimisation and Quadrature (ALOQ), which uses Bayesian optimisation and Bayesian quadrature to address such settings. ALOQ is robust to the presence of significant rare events, which may not be observable under random sampling, but play a substantial role in determining the optimal policy. Experimental results across different domains show that ALOQ can learn more efficiently and robustly than existing methods.

cs.LG↗

arXiv2017

Gaussian Process Regression for In-situ Capacity Estimation of Lithium-ion Batteries

Accurate on-board capacity estimation is of critical importance in lithium-ion battery applications. Battery charging/discharging often occurs under a constant current load, and hence voltage vs. time measurements under this condition may be accessible in practice. This paper presents a data-driven diagnostic technique, Gaussian Process regression for In-situ Capacity Estimation (GP-ICE), which estimates battery capacity using voltage measurements over short periods of galvanostatic operation. Unlike previous works, GP-ICE does not rely on interpreting the voltage-time data as Incremental Capacity (IC) or Differential Voltage (DV) curves. This overcomes the need to differentiate the voltage-time data (a process which amplifies measurement noise), and the requirement that the range of voltage measurements encompasses the peaks in the IC/DV curves. GP-ICE is applied to two datasets, consisting of 8 and 20 cells respectively. In each case, within certain voltage ranges, as little as 10 seconds of galvanostatic operation enables capacity estimates with approximately 2-3% RMSE.

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arXiv2017

Probabilistic Integration: A Role in Statistical Computation?

A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly deterministic) computational work-flow. This paper examines the case for probabilistic numerical methods in routine statistical computation. Our focus is on numerical integration, where a probabilistic integrator is equipped with a full distribution over its output that reflects the presence of an unknown numerical error. Our main technical contribution is to establish, for the first time, rates of posterior contraction for these methods. These show that probabilistic integrators can in principle enjoy the "best of both worlds", leveraging the sampling efficiency of Monte Carlo methods whilst providing a principled route to assess the impact of numerical error on scientific conclusions. Several substantial applications are provided for illustration and critical evaluation, including examples from statistical modelling, computer graphics and a computer model for an oil reservoir.

stat.ML↗

arXiv2017

Bayesian Optimization for Probabilistic Programs

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any graphical model, can be optimized with respect to an arbitrary subset of its sampled variables. To carry out this optimization, we develop the first Bayesian optimization package to directly exploit the source code of its target, leading to innovations in problem-independent hyperpriors, unbounded optimization, and implicit constraint satisfaction; delivering significant performance improvements over prominent existing packages. We present applications of our method to a number of tasks including engineering design and parameter optimization.

stat.ML↗

arXiv2017

Gaussian process regression for forecasting battery state of health

Accurately predicting the future capacity and remaining useful life of batteries is necessary to ensure reliable system operation and to minimise maintenance costs. The complex nature of battery degradation has meant that mechanistic modelling of capacity fade has thus far remained intractable; however, with the advent of cloud-connected devices, data from cells in various applications is becoming increasingly available, and the feasibility of data-driven methods for battery prognostics is increasing. Here we propose Gaussian process (GP) regression for forecasting battery state of health, and highlight various advantages of GPs over other data-driven and mechanistic approaches. GPs are a type of Bayesian non-parametric method, and hence can model complex systems whilst handling uncertainty in a principled manner. Prior information can be exploited by GPs in a variety of ways: explicit mean functions can be used if the functional form of the underlying degradation model is available, and multiple-output GPs can effectively exploit correlations between data from different cells. We demonstrate the predictive capability of GPs for short-term and long-term (remaining useful life) forecasting on a selection of capacity vs. cycle datasets from lithium-ion cells.

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