We present a developmental framework based on a long-term memory and reasoning mechanisms (Vision Similarity and Bayesian Optimisation). This architecture allows a robot to optimize autonomously hyper-parameters that need to be tuned from any action and/or vision module, treated as a black-box. The learning can take advantage of past experiences (stored in the episodic and procedural memories) in order to warm-start the exploration using a set of hyper-parameters previously optimized from objects similar to the new unknown one (stored in a semantic memory). As example, the system has been used to optimized 9 continuous hyper-parameters of a professional software (Kamido) both in simulation and with a real robot (industrial robotic arm Fanuc) with a total of 13 different objects. The robot is able to find a good object-specific optimization in 68 (simulation) or 40 (real) trials. In simulation, we demonstrate the benefit of the transfer learning based on visual similarity, as opposed to an amnesic learning (i.e. learning from scratch all the time). Moreover, with the real robot, we show that the method consistently outperforms the manual optimization from an expert with less than 2 hours of training time to achieve more than 88% of success.
Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a functional optimisation problem. We develop a novel Bayesian optimisation framework for such functional optimisation of expensive black-box processes. We represent the control function using Bernstein polynomial basis and optimise in the coefficient space. We derive the theory and practice required to dynamically adjust the order of the polynomial degree, and show how prior information about shape can be integrated. We demonstrate the effectiveness of our approach for short polymer fibre design and optimising learning rate schedules for deep networks.
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard. While reasonable practical solutions have been advanced, they can often fail to find the best optima. Surprisingly, there is little theoretical analysis of this crucial problem in the literature. To address this, we derive a cumulative regret bound for Bayesian optimisation with Gaussian processes and unknown kernel hyper-parameters in the stochastic setting. The bound, which applies to the expected improvement acquisition function and sub-Gaussian observation noise, provides us with guidelines on how to design hyper-parameter estimation methods. A simple simulation demonstrates the importance of following these guidelines.
We introduce a means of automating machine learning (ML) for big data tasks, by performing scalable stochastic Bayesian optimisation of ML algorithm parameters and hyper-parameters. More often than not, the critical tuning of ML algorithm parameters has relied on domain expertise from experts, along with laborious hand-tuning, brute search or lengthy sampling runs. Against this background, Bayesian optimisation is finding increasing use in automating parameter tuning, making ML algorithms accessible even to non-experts. However, the state of the art in Bayesian optimisation is incapable of scaling to the large number of evaluations of algorithm performance required to fit realistic models to complex, big data. We here describe a stochastic, sparse, Bayesian optimisation strategy to solve this problem, using many thousands of noisy evaluations of algorithm performance on subsets of data in order to effectively train algorithms for big data. We provide a comprehensive benchmarking of possible sparsification strategies for Bayesian optimisation, concluding that a Nystrom approximation offers the best scaling and performance for real tasks. Our proposed algorithm demonstrates substantial improvement over the state of the art in tuning the parameters of a Gaussian Process time series prediction task on real, big data.
This paper presents novel Bayesian optimisation algorithms for minimum error rate training of statistical machine translation systems. We explore two classes of algorithms for efficiently exploring the translation space, with the first based on N-best lists and the second based on a hypergraph representation that compactly represents an exponential number of translation options. Our algorithms exhibit faster convergence and are capable of obtaining lower error rates than the existing translation model specific approaches, all within a generic Bayesian optimisation framework. Further more, we also introduce a random embedding algorithm to scale our approach to sparse high dimensional feature sets.
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.
The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only allow the exploration of the parameter space to occur sequentially. Often, it is desirable to simultaneously propose batches of parameter values to explore. This is particularly the case when large parallel processing facilities are available. These facilities could be computational or physical facets of the process being optimized. E.g. in biological experiments many experimental set ups allow several samples to be simultaneously processed. Batch methods, however, require modeling of the interaction between the evaluations in the batch, which can be expensive in complex scenarios. We investigate a simple heuristic based on an estimate of the Lipschitz constant that captures the most important aspect of this interaction (i.e. local repulsion) at negligible computational overhead. The resulting algorithm compares well, in running time, with much more elaborate alternatives. The approach assumes that the function of interest, $f$, is a Lipschitz continuous function. A wrap-loop around the acquisition function is used to collect batches of points of certain size minimizing the non-parallelizable computational effort. The speed-up of our method with respect to previous approaches is significant in a set of computationally expensive experiments.
We present GLASSES: Global optimisation with Look-Ahead through Stochastic Simulation and Expected-loss Search. The majority of global optimisation approaches in use are myopic, in only considering the impact of the next function value; the non-myopic approaches that do exist are able to consider only a handful of future evaluations. Our novel algorithm, GLASSES, permits the consideration of dozens of evaluations into the future. This is done by approximating the ideal look-ahead loss function, which is expensive to evaluate, by a cheaper alternative in which the future steps of the algorithm are simulated beforehand. An Expectation Propagation algorithm is used to compute the expected value of the loss.We show that the far-horizon planning thus enabled leads to substantive performance gains in empirical tests.
A long-lived autonomous agent should be able to respond online to novel instances of tasks from a familiar domain. Acting online requires 'fast' responses, in terms of rapid convergence, especially when the task instance has a short duration, such as in applications involving interactions with humans. These requirements can be problematic for many established methods for learning to act. In domains where the agent knows that the task instance is drawn from a family of related tasks, albeit without access to the label of any given instance, it can choose to act through a process of policy reuse from a library, rather than policy learning from scratch. In policy reuse, the agent has prior knowledge of the class of tasks in the form of a library of policies that were learnt from sample task instances during an offline training phase. We formalise the problem of policy reuse, and present an algorithm for efficiently responding to a novel task instance by reusing a policy from the library of existing policies, where the choice is based on observed 'signals' which correlate to policy performance. We achieve this by posing the problem as a Bayesian choice problem with a corresponding notion of an optimal response, but the computation of that response is in many cases intractable. Therefore, to reduce the computation cost of the posterior, we follow a Bayesian optimisation approach and define a set of policy selection functions, which balance exploration in the policy library against exploitation of previously tried policies, together with a model of expected performance of the policy library on their corresponding task instances. We validate our method in several simulated domains of interactive, short-duration episodic tasks, showing rapid convergence in unknown task variations.
Bayesian Optimisation (BO) is a technique used in optimising a $D$-dimensional function which is typically expensive to evaluate. While there have been many successes for BO in low dimensions, scaling it to high dimensions has been notoriously difficult. Existing literature on the topic are under very restrictive settings. In this paper, we identify two key challenges in this endeavour. We tackle these challenges by assuming an additive structure for the function. This setting is substantially more expressive and contains a richer class of functions than previous work. We prove that, for additive functions the regret has only linear dependence on $D$ even though the function depends on all $D$ dimensions. We also demonstrate several other statistical and computational benefits in our framework. Via synthetic examples, a scientific simulation and a face detection problem we demonstrate that our method outperforms naive BO on additive functions and on several examples where the function is not additive.
Bandit methods for black-box optimisation, such as Bayesian optimisation, are used in a variety of applications including hyper-parameter tuning and experiment design. Recently, \emph{multi-fidelity} methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multi-fidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multi-fidelity methods assume only a finite number of approximations. In many practical applications however, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data $N$ and/or few training iterations $T$. Here, the approximations are best viewed as arising out of a continuous two dimensional space $(N,T)$. In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.
We design and analyse variations of the classical Thompson sampling (TS) procedure for Bayesian optimisation (BO) in settings where function evaluations are expensive, but can be performed in parallel. Our theoretical analysis shows that a direct application of the sequential Thompson sampling algorithm in either synchronous or asynchronous parallel settings yields a surprisingly powerful result: making $n$ evaluations distributed among $M$ workers is essentially equivalent to performing $n$ evaluations in sequence. Further, by modeling the time taken to complete a function evaluation, we show that, under a time constraint, asynchronously parallel TS achieves asymptotically lower regret than both the synchronous and sequential versions. These results are complemented by an experimental analysis, showing that asynchronous TS outperforms a suite of existing parallel BO algorithms in simulations and in a hyper-parameter tuning application in convolutional neural networks. In addition to these, the proposed procedure is conceptually and computationally much simpler than existing work for parallel BO.
We consider the problem of approximate Bayesian parameter inference in non-linear state-space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is one approach to approximate the likelihood in this type of models. However, such approximations can be noisy and computationally costly which hinders efficient implementations using standard methods based on optimisation and Monte Carlo methods. We propose a computationally efficient novel method based on the combination of Gaussian process optimisation and SMC-ABC to create a Laplace approximation of the intractable posterior. We exemplify the proposed algorithm for inference in stochastic volatility models with both synthetic and real-world data as well as for estimating the Value-at-Risk for two portfolios using a copula model. We document speed-ups of between one and two orders of magnitude compared to state-of-the-art algorithms for posterior inference.
Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is only one of several metrics that must be considered when optimizing random forest parameters for commercial applications. We propose a novel metric that captures the stability of random forests predictions, which we argue is key for scenarios that require successive predictions. We motivate the need for multi-criteria optimization by showing that in practical applications, simply choosing the parameters that lead to the lowest error can introduce unnecessary costs and produce predictions that are not stable across independent runs. To optimize this multi-criteria trade-off, we present a new framework that efficiently finds a principled balance between these three considerations using Bayesian optimisation. The pitfalls of optimising forest parameters purely for error reduction are demonstrated using two publicly available real world datasets. We show that our framework leads to parameter settings that are markedly different from the values discovered by error reduction metrics.
Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.
The Lobula Giant Movement Detector (LGMD) is a an identified neuron of the locust that detects looming objects and triggers its escape responses. Understanding the neural principles and networks that lead to these fast and robust responses can lead to the design of efficient facilitate obstacle avoidance strategies in robotic applications. Here we present a neuromorphic spiking neural network model of the LGMD driven by the output of a neuromorphic Dynamic Vision Sensor (DVS), which has been optimised to produce robust and reliable responses in the face of the constraints and variability of its mixed signal analogue-digital circuits. As this LGMD model has many parameters, we use the Differential Evolution (DE) algorithm to optimise its parameter space. We also investigate the use of Self-Adaptive Differential Evolution (SADE) which has been shown to ameliorate the difficulties of finding appropriate input parameters for DE. We explore the use of two biological mechanisms: synaptic plasticity and membrane adaptivity in the LGMD. We apply DE and SADE to find parameters best suited for an obstacle avoidance system on an unmanned aerial vehicle (UAV), and show how it outperforms state-of-the-art Bayesian optimisation used for comparison.
A novel Python framework for Bayesian optimization known as GPflowOpt is introduced. The package is based on the popular GPflow library for Gaussian processes, leveraging the benefits of TensorFlow including automatic differentiation, parallelization and GPU computations for Bayesian optimization. Design goals focus on a framework that is easy to extend with custom acquisition functions and models. The framework is thoroughly tested and well documented, and provides scalability. The current released version of GPflowOpt includes some standard single-objective acquisition functions, the state-of-the-art max-value entropy search, as well as a Bayesian multi-objective approach. Finally, it permits easy use of custom modeling strategies implemented in GPflow.
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.
Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computation for estimating entropies. We propose a new criterion, Max-value Entropy Search (MES), that instead uses the information about the maximum function value. We show relations of MES to other Bayesian optimization methods, and establish a regret bound. We observe that MES maintains or improves the good empirical performance of ES/PES, while tremendously lightening the computational burden. In particular, MES is much more robust to the number of samples used for computing the entropy, and hence more efficient for higher dimensional problems.
The discovery of processes for the synthesis of new materials involves many decisions about process design, operation, and material properties. Experimentation is crucial but as complexity increases, exploration of variables can become impractical using traditional combinatorial approaches. We describe an iterative method which uses machine learning to optimise process development, incorporating multiple qualitative and quantitative objectives. We demonstrate the method with a novel fluid processing platform for synthesis of short polymer fibers, and show how the synthesis process can be efficiently directed to achieve material and process objectives.