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Funneled Bayesian Optimization for Design, Tuning and Control of Autonomous Systems

arXiv.org Machine Learning

Bayesian optimization has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. Recently, there has been proposed a large number of new applications in fields such as robotics, machine learning, experimental design, simulation, etc. In this paper, we focus on several problems that appear in robotics and autonomous systems: algorithm tuning, automatic control and intelligent design. All those problems can be mapped to global optimization problems. However, they become hard optimization problems. Bayesian optimization internally uses a probabilistic surrogate model (e.g.: Gaussian process) to learn from the process and reduce the number of samples required. In order to generalize to unknown functions in a black-box fashion, the common assumption is that the underlying function can be modeled with a stationary process. Nonstationary Gaussian process regression cannot generalize easily and it typically requires prior knowledge of the function. Some works have designed techniques to generalize Bayesian optimization to nonstationary functions in an indirect way, but using techniques originally designed for regression, where the objective is to improve the quality of the surrogate model everywhere. Instead optimization should focus on improving the surrogate model near the optimum. In this paper, we present a novel kernel function specially designed for Bayesian optimization, that allows nonstationary behavior of the surrogate model in an adaptive local region. In our experiments, we found that this new kernel results in an improved local search (exploitation), without penalizing the global search (exploration). We provide results in well-known benchmarks and real applications. The new method outperforms the state of the art in Bayesian optimization both in stationary and nonstationary problems.


Local Nonstationarity for Efficient Bayesian Optimization

arXiv.org Machine Learning

Bayesian optimization has shown to be a fundamental global optimization algorithm in many applications: ranging from automatic machine learning, robotics, reinforcement learning, experimental design, simulations, etc. The most popular and effective Bayesian optimization relies on a surrogate model in the form of a Gaussian process due to its flexibility to represent a prior over function. However, many algorithms and setups relies on the stationarity assumption of the Gaussian process. In this paper, we present a novel nonstationary strategy for Bayesian optimization that is able to outperform the state of the art in Bayesian optimization both in stationary and nonstationary problems.


Practical Bayesian optimization in the presence of outliers

arXiv.org Machine Learning

Inference in the presence of outliers is an important field of research as outliers are ubiquitous and may arise across a variety of problems and domains. Bayesian optimization is method that heavily relies on probabilistic inference. This allows outstanding sample efficiency because the probabilistic machinery provides a memory of the whole optimization process. However, that virtue becomes a disadvantage when the memory is populated with outliers, inducing bias in the estimation. In this paper, we present an empirical evaluation of Bayesian optimization methods in the presence of outliers. The empirical evidence shows that Bayesian optimization with robust regression often produces suboptimal results. We then propose a new algorithm which combines robust regression (a Gaussian process with Student-t likelihood) with outlier diagnostics to classify data points as outliers or inliers. By using an scheduler for the classification of outliers, our method is more efficient and has better convergence over the standard robust regression. Furthermore, we show that even in controlled situations with no expected outliers, our method is able to produce better results.


High-Dimensional Bayesian Optimization with Manifold Gaussian Processes

arXiv.org Machine Learning

Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. The Bayesian optimization routine involves learning a response surface and maximizing a score to select the most valuable inputs to be queried at the next iteration. These key steps are subject to the curse of dimensionality so that Bayesian optimization does not scale beyond 10--20 parameters. In this work, we address this issue and propose a high-dimensional BO method that learns a nonlinear low-dimensional manifold of the input space. We achieve this with a multi-layer neural network embedded in the covariance function of a Gaussian process. This approach applies unsupervised dimensionality reduction as a byproduct of a supervised regression solution. This also allows exploiting data efficiency of Gaussian process models in a Bayesian framework. We also introduce a nonlinear mapping from the manifold to the high-dimensional space based on multi-output Gaussian processes and jointly train it end-to-end via marginal likelihood maximization. We show this intrinsically low-dimensional optimization outperforms recent baselines in high-dimensional BO literature on a set of benchmark functions in 60 dimensions.


Robust Policy Search for Robot Navigation with Stochastic Meta-Policies

arXiv.org Machine Learning

Bayesian optimization is an efficient nonlinear optimization method where the queries are carefully selected to gather information about the optimum location. Thus, in the context of policy search, it has been called active policy search. The main ingredients of Bayesian optimization for sample efficiency are the probabilistic surrogate model and the optimal decision heuristics. In this work, we exploit those to provide robustness to different issues for policy search algorithms. We combine several methods and show how their interaction works better than the sum of the parts. First, to deal with input noise and provide a safe and repeatable policy we use an improved version of unscented Bayesian optimization. Then, to deal with mismodeling errors and improve exploration we use stochastic meta-policies for query selection and an adaptive kernel. We compare the proposed algorithm with previous results in several optimization benchmarks and robot tasks, such as pushing objects with a robot arm, or path finding with a rover.