12 research outputs found
Bayesian Optimisation for Safe Navigation under Localisation Uncertainty
In outdoor environments, mobile robots are required to navigate through
terrain with varying characteristics, some of which might significantly affect
the integrity of the platform. Ideally, the robot should be able to identify
areas that are safe for navigation based on its own percepts about the
environment while avoiding damage to itself. Bayesian optimisation (BO) has
been successfully applied to the task of learning a model of terrain
traversability while guiding the robot through more traversable areas. An
issue, however, is that localisation uncertainty can end up guiding the robot
to unsafe areas and distort the model being learnt. In this paper, we address
this problem and present a novel method that allows BO to consider localisation
uncertainty by applying a Gaussian process model for uncertain inputs as a
prior. We evaluate the proposed method in simulation and in experiments with a
real robot navigating over rough terrain and compare it against standard BO
methods.Comment: To appear in the proceedings of the 18th International Symposium on
Robotics Research (ISRR 2017
Robust Bayesian Satisficing
Distributional shifts pose a significant challenge to achieving robustness in
contemporary machine learning. To overcome this challenge, robust satisficing
(RS) seeks a robust solution to an unspecified distributional shift while
achieving a utility above a desired threshold. This paper focuses on the
problem of RS in contextual Bayesian optimization when there is a discrepancy
between the true and reference distributions of the context. We propose a novel
robust Bayesian satisficing algorithm called RoBOS for noisy black-box
optimization. Our algorithm guarantees sublinear lenient regret under certain
assumptions on the amount of distribution shift. In addition, we define a
weaker notion of regret called robust satisficing regret, in which our
algorithm achieves a sublinear upper bound independent of the amount of
distribution shift. To demonstrate the effectiveness of our method, we apply it
to various learning problems and compare it to other approaches, such as
distributionally robust optimization
Distributionally Robust Bayesian Optimization
Robustness to distributional shift is one of the key challenges of
contemporary machine learning. Attaining such robustness is the goal of
distributionally robust optimization, which seeks a solution to an optimization
problem that is worst-case robust under a specified distributional shift of an
uncontrolled covariate. In this paper, we study such a problem when the
distributional shift is measured via the maximum mean discrepancy (MMD). For
the setting of zeroth-order, noisy optimization, we present a novel
distributionally robust Bayesian optimization algorithm (DRBO). Our algorithm
provably obtains sub-linear robust regret in various settings that differ in
how the uncertain covariate is observed. We demonstrate the robust performance
of our method on both synthetic and real-world benchmarks.Comment: Accepted at AISTATS 202
Robust expected improvement for Bayesian optimization
Bayesian Optimization (BO) links Gaussian Process (GP) surrogates with
sequential design toward optimizing expensive-to-evaluate black-box functions.
Example design heuristics, or so-called acquisition functions, like expected
improvement (EI), balance exploration and exploitation to furnish global
solutions under stringent evaluation budgets. However, they fall short when
solving for robust optima, meaning a preference for solutions in a wider domain
of attraction. Robust solutions are useful when inputs are imprecisely
specified, or where a series of solutions is desired. A common mathematical
programming technique in such settings involves an adversarial objective,
biasing a local solver away from ``sharp'' troughs. Here we propose a surrogate
modeling and active learning technique called robust expected improvement (REI)
that ports adversarial methodology into the BO/GP framework. After describing
the methods, we illustrate and draw comparisons to several competitors on
benchmark synthetic exercises and real problems of varying complexity.Comment: 27 pages, 17 figures, 1 tabl