Are we Forgetting about Compositional Optimisers in Bayesian Optimisation?

Bayesian optimisation presents a sample-efficient methodology for global optimisation. Within this framework, a crucial performance-determining subroutine is the maximisation of the acquisition function, a task complicated by the fact that acquisition functions tend to be non-convex and thus nontrivial to optimise. In this paper, we undertake a comprehensive empirical study of approaches to maximise the acquisition function. Additionally, by deriving novel, yet mathematically equivalent, compositional forms for popular acquisition functions, we recast the maximisation task as a compositional optimisation problem, allowing us to benefit from the extensive literature in this field. We highlight the empirical advantages of the compositional approach to acquisition function maximisation across 3958 individual experiments comprising synthetic optimisation tasks as well as tasks from Bayesmark. Given the generality of the acquisition function maximisation subroutine, we posit that the adoption of compositional optimisers has the potential to yield performance improvements across all domains in which Bayesian optimisation is currently being applied. An open-source implementation is made available at https://github.com/huawei-noah/noah-research/tree/CompBO/BO/HEBO/CompBO

Decision-making with gaussian processes: sampling strategies and monte carlo methods

We study Gaussian processes and their application to decision-making in the real world. We begin by reviewing the foundations of Bayesian decision theory and show how these ideas give rise to methods such as Bayesian optimization. We investigate practical techniques for carrying out these strategies, with an emphasis on estimating and maximizing acquisition functions. Finally, we introduce pathwise approaches to conditioning Gaussian processes and demonstrate key benefits for representing random variables in this manner.Open Acces

Novel Memetic Computing Structures for Continuous Optimisation

This thesis studies a class of optimisation algorithms, namely Memetic Computing Structures, and proposes a novel set of promising algorithms that move the first step towards an implementation for the automatic generation of optimisation algorithms for continuous domains. This thesis after a thorough review of local search algorithms and popular meta-heuristics, focuses on Memetic Computing in terms of algorithm structures and design philosophy. In particular, most of the design carried out during my doctoral studies is inspired by the lex parsimoniae, aka Ockham’s Razor. It has been shown how simple algorithms, when well implemented can outperform complex implementations. In order to achieve this aim, the design is always carried out by attempting to identify the role of each algorithmic component/operator. In this thesis, on the basis of this logic, a set of variants of a recently proposed algorithms are presented. Subsequently a novel memetic structure, namely Parallel Memetic Structure is proposed and tested against modern algorithms representing the state of the art in optimisation. Furthermore, an initial prototype of an automatic design platform is also included. This prototype performs an analysis on separability of the optimisation problem and, on the basis of the analysis results, designs some parts of the parallel structure. Promising results are included. Finally, an investigation of the correlation among the variables and problem dimensionality has been performed. An extremely interesting finding of this thesis work is that the degree of correlation among the variables decreases when the dimensionality increases. As a direct consequence of this fact, large scale problems are to some extent easier to handle than problems in low dimensionality since, due to the lack of correlation among the variables, they can effectively be tackled by an algorithm that performs moves along the axes

Applied (Meta)-Heuristic in Intelligent Systems

Engineering and business problems are becoming increasingly difficult to solve due to the new economics triggered by big data, artificial intelligence, and the internet of things. Exact algorithms and heuristics are insufficient for solving such large and unstructured problems; instead, metaheuristic algorithms have emerged as the prevailing methods. A generic metaheuristic framework guides the course of search trajectories beyond local optimality, thus overcoming the limitations of traditional computation methods. The application of modern metaheuristics ranges from unmanned aerial and ground surface vehicles, unmanned factories, resource-constrained production, and humanoids to green logistics, renewable energy, circular economy, agricultural technology, environmental protection, finance technology, and the entertainment industry. This Special Issue presents high-quality papers proposing modern metaheuristics in intelligent systems

Hybrid solutions to instantaneous MIMO blind separation and decoding: narrowband, QAM and square cases

Future wireless communication systems are desired to support high data rates and high quality transmission when considering the growing multimedia applications. Increasing the channel throughput leads to the multiple input and multiple output and blind equalization techniques in recent years. Thereby blind MIMO equalization has attracted a great interest.Both system performance and computational complexities play important roles in real time communications. Reducing the computational load and providing accurate performances are the main challenges in present systems. In this thesis, a hybrid method which can provide an affordable complexity with good performance for Blind Equalization in large constellation MIMO systems is proposed first. Saving computational cost happens both in the signal sep- aration part and in signal detection part. First, based on Quadrature amplitude modulation signal characteristics, an efficient and simple nonlinear function for the Independent Compo- nent Analysis is introduced. Second, using the idea of the sphere decoding, we choose the soft information of channels in a sphere, and overcome the so- called curse of dimensionality of the Expectation Maximization (EM) algorithm and enhance the final results simultaneously. Mathematically, we demonstrate in the digital communication cases, the EM algorithm shows Newton -like convergence.Despite the widespread use of forward -error coding (FEC), most multiple input multiple output (MIMO) blind channel estimation techniques ignore its presence, and instead make the sim- plifying assumption that the transmitted symbols are uncoded. However, FEC induces code structure in the transmitted sequence that can be exploited to improve blind MIMO channel estimates. In final part of this work, we exploit the iterative channel estimation and decoding performance for blind MIMO equalization. Experiments show the improvements achievable by exploiting the existence of coding structures and that it can access the performance of a BCJR equalizer with perfect channel information in a reasonable SNR range. All results are confirmed experimentally for the example of blind equalization in block fading MIMO systems

Kernel methods for Monte Carlo

This thesis investigates the use of reproducing kernel Hilbert spaces (RKHS) in the context of Monte Carlo algorithms. The work proceeds in three main themes. Adaptive Monte Carlo proposals: We introduce and study two adaptive Markov chain Monte Carlo (MCMC) algorithms to sample from target distributions with non-linear support and intractable gradients. Our algorithms, generalisations of random walk Metropolis and Hamiltonian Monte Carlo, adaptively learn local covariance and gradient structure respectively, by modelling past samples in an RKHS. We further show how to embed these methods into the sequential Monte Carlo framework. Efficient and principled score estimation: We propose methods for fitting an RKHS exponential family model that work by fitting the gradient of the log density, the score, thus avoiding the need to compute a normalization constant. While the problem is of general interest, here we focus on its embedding into the adaptive MCMC context from above. We improve the computational efficiency of an earlier solution with two novel fast approximation schemes without guarantees, and a low-rank, Nyström-like solution. The latter retains the consistency and convergence rates of the exact solution, at lower computational cost. Goodness-of-fit testing: We propose a non-parametric statistical test for goodness-of-fit. The measure is a divergence constructed via Stein's method using functions from an RKHS. We derive a statistical test, both for i.i.d. and non-i.i.d. samples, and apply the test to quantifying convergence of approximate MCMC methods, statistical model criticism, and evaluating accuracy in non-parametric score estimation