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Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in…
We consider a sequential decision making task where we are not allowed to evaluate parameters that violate an a priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on the unknown constraint and allow…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…
This paper proposes a safe data-driven control framework for nonlinear systems with partially known dynamics. The method ensures stability and constraint satisfaction during online learning, assuming only a stabilizable linear approximation…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
In this paper, we consider the problem of using a robot to explore an environment with an unknown, state-dependent disturbance function while avoiding some forbidden areas. The goal of the robot is to safely collect observations of the…
Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…
In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of…
In Gaussian Process (GP) dynamical model learning for robot control, particularly for systems constrained by computational resources like small quadrotors equipped with low-end processors, analyzing stability and designing a stable…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
Safety is one of the biggest concerns to applying reinforcement learning (RL) to the physical world. In its core part, it is challenging to ensure RL agents persistently satisfy a hard state constraint without white-box or black-box…
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
We present a chance-constrained model predictive control (MPC) framework under Gaussian mixture model (GMM) uncertainty. Specifically, we consider the uncertainty that arises from predicting future behaviors of moving obstacles, which may…
We propose a model predictive control approach for autonomous vehicles that exploits learned Gaussian processes for predicting human driving behavior. The proposed approach employs the uncertainty about the GP's prediction to achieve…
Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…
Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated…
The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility…