Safety in safe Bayesian optimization and its ramifications for control

A recurring and important task in control engineering is parameter tuning under constraints, which conceptually amounts to optimization of a blackbox function accessible only through noisy evaluations. For example, in control practice parameters of a pre-designed controller are often tuned online in feedback with a plant, and only safe parameter values should be tried, avoiding for example instability. Recently, machine learning methods have been deployed for this important problem, in particular, Bayesian optimization (BO). To handle safety constraints, algorithms from safe BO have been utilized, especially SafeOpt-type algorithms, which enjoy considerable popularity in learning-based control, robotics, and adjacent fields. However, we identify two significant obstacles to practical safety. First, SafeOpt-type algorithms rely on quantitative uncertainty bounds, and most implementations replace these by theoretically unsupported heuristics. Second, the theoretically valid uncertainty bounds crucially depend on a quantity - the reproducing kernel Hilbert space norm of the target function - that at present is impossible to reliably bound using established prior engineering knowledge. By careful numerical experiments we show that these issues can indeed cause safety violations. To overcome these problems, we propose Lipschitz-only Safe Bayesian Optimization (LoSBO), a safe BO algorithm that relies only on a known Lipschitz bound for its safety. Furthermore, we propose a variant (LoS-GP-UCB) that avoids gridding of the search space and is therefore applicable even for moderately high-dimensional problems.

CHEQ-ing the Box: Safe Variable Impedance Learning for Robotic Polishing

Robotic systems are increasingly employed for industrial automation, with contact-rich tasks like polishing requiring dexterity and compliant behaviour. These tasks are difficult to model, making classical control challenging. Deep reinforcement learning (RL) offers a promising solution by enabling the learning of models and control policies directly from data. However, its application to real-world problems is limited by data inefficiency and unsafe exploration. Adaptive hybrid RL methods blend classical control and RL adaptively, combining the strengths of both: structure from control and learning from RL. This has led to improvements in data efficiency and exploration safety. However, their potential for hardware applications remains underexplored, with no evaluations on physical systems to date. Such evaluations are critical to fully assess the practicality and effectiveness of these methods in real-world settings. This work presents an experimental demonstration of the hybrid RL algorithm CHEQ for robotic polishing with variable impedance, a task requiring precise force and velocity tracking. In simulation, we show that variable impedance enhances polishing performance. We compare standalone RL with adaptive hybrid RL, demonstrating that CHEQ achieves effective learning while adhering to safety constraints. On hardware, CHEQ achieves effective polishing behaviour, requiring only eight hours of training and incurring just five failures. These results highlight the potential of adaptive hybrid RL for real-world, contact-rich tasks trained directly on hardware.

Bayesian Optimization via Continual Variational Last Layer Training

Gaussian Processes (GPs) are widely seen as the state-of-the-art surrogate models for Bayesian optimization (BO) due to their ability to model uncertainty and their performance on tasks where correlations are easily captured (such as those defined by Euclidean metrics) and their ability to be efficiently updated online. However, the performance of GPs depends on the choice of kernel, and kernel selection for complex correlation structures is often difficult or must be made bespoke. While Bayesian neural networks (BNNs) are a promising direction for higher capacity surrogate models, they have so far seen limited use due to poor performance on some problem types. In this paper, we propose an approach which shows competitive performance on many problem types, including some that BNNs typically struggle with. We build on variational Bayesian last layers (VBLLs), and connect training of these models to exact conditioning in GPs. We exploit this connection to develop an efficient online training algorithm that interleaves conditioning and optimization. Our findings suggest that VBLL networks significantly outperform GPs and other BNN architectures on tasks with complex input correlations, and match the performance of well-tuned GPs on established benchmark tasks.

On Foundation Models for Dynamical Systems from Purely Synthetic Data

Foundation models have demonstrated remarkable generalization, data efficiency, and robustness properties across various domains. In this paper, we explore the feasibility of foundation models for applications in the control domain. The success of these models is enabled by large-scale pretaining on Internet-scale datasets. These are available in fields like natural language processing and computer vision, but do not exist for dynamical systems. We address this challenge by pretraining a transformer-based foundation model exclusively on synthetic data and propose to sample dynamics functions from a reproducing kernel Hilbert space. Our pretrained model generalizes for prediction tasks across different dynamical systems, which we validate in simulation and hardware experiments, including cart-pole and Furuta pendulum setups. Additionally, the model can be fine-tuned effectively to new systems to increase performance even further. Our results demonstrate the feasibility of foundation models for dynamical systems that outperform specialist models in terms of generalization, data efficiency, and robustness.

Local Bayesian Optimization for Controller Tuning with Crash Constraints

Controller tuning is crucial for closed-loop performance but often involves manual adjustments. Although Bayesian optimization (BO) has been established as a data-efficient method for automated tuning, applying it to large and high-dimensional search spaces remains challenging. We extend a recently proposed local variant of BO to include crash constraints, where the controller can only be successfully evaluated in an a-priori unknown feasible region. We demonstrate the efficiency of the proposed method through simulations and hardware experiments. Our findings showcase the potential of local BO to enhance controller performance and reduce the time and resources necessary for tuning.

Simulation-Aided Policy Tuning for Black-Box Robot Learning

How can robots learn and adapt to new tasks and situations with little data? Systematic exploration and simulation are crucial tools for efficient robot learning. We present a novel black-box policy search algorithm focused on data-efficient policy improvements. The algorithm learns directly on the robot and treats simulation as an additional information source to speed up the learning process. At the core of the algorithm, a probabilistic model learns the dependence of the policy parameters and the robot learning objective not only by performing experiments on the robot, but also by leveraging data from a simulator. This substantially reduces interaction time with the robot. Using this model, we can guarantee improvements with high probability for each policy update, thereby facilitating fast, goal-oriented learning. We evaluate our algorithm on simulated fine-tuning tasks and demonstrate the data-efficiency of the proposed dual-information source optimization algorithm. In a real robot learning experiment, we show fast and successful task learning on a robot manipulator with the aid of an imperfect simulator.

Feedforward Controllers from Learned Dynamic Local Model Networks with Application to Excavator Assistance Functions

Complicated first principles modelling and controller synthesis can be prohibitively slow and expensive for high-mix, low-volume products such as hydraulic excavators. Instead, in a data-driven approach, recorded trajectories from the real system can be used to train local model networks (LMNs), for which feedforward controllers are derived via feedback linearization. However, previous works required LMNs without zero dynamics for feedback linearization, which restricts the model structure and thus modelling capacity of LMNs. In this paper, we overcome this restriction by providing a criterion for when feedback linearization of LMNs with zero dynamics yields a valid controller. As a criterion we propose the bounded-input bounded-output stability of the resulting controller. In two additional contributions, we extend this approach to consider measured disturbance signals and multiple inputs and outputs. We illustrate the effectiveness of our contributions in a hydraulic excavator control application with hardware experiments. To this end, we train LMNs from recorded, noisy data and derive feedforward controllers used as part of a leveling assistance system on the excavator. In our experiments, incorporating disturbance signals and multiple inputs and outputs enhances tracking performance of the learned controller. A video of our experiments is available at https://youtu.be/lrrWBx2ASaE.

Learning deformable linear object dynamics from a single trajectory

The manipulation of deformable linear objects (DLOs) via model-based control requires an accurate and computationally efficient dynamics model. Yet, data-driven DLO dynamics models require large training data sets while their predictions often do not generalize, whereas physics-based models rely on good approximations of physical phenomena and often lack accuracy. To address these challenges, we propose a physics-informed neural ODE capable of predicting agile movements with significantly less data and hyper-parameter tuning. In particular, we model DLOs as serial chains of rigid bodies interconnected by passive elastic joints in which interaction forces are predicted by neural networks. The proposed model accurately predicts the motion of an robotically-actuated aluminium rod and an elastic foam cylinder after being trained on only thirty seconds of data. The project code and data are available at: \url{https://tinyurl.com/neuralprba}

Contextualized Hybrid Ensemble Q-learning: Learning Fast with Control Priors

Combining Reinforcement Learning (RL) with a prior controller can yield the best out of two worlds: RL can solve complex nonlinear problems, while the control prior ensures safer exploration and speeds up training. Prior work largely blends both components with a fixed weight, neglecting that the RL agent's performance varies with the training progress and across regions in the state space. Therefore, we advocate for an adaptive strategy that dynamically adjusts the weighting based on the RL agent's current capabilities. We propose a new adaptive hybrid RL algorithm, Contextualized Hybrid Ensemble Q-learning (CHEQ). CHEQ combines three key ingredients: (i) a time-invariant formulation of the adaptive hybrid RL problem treating the adaptive weight as a context variable, (ii) a weight adaption mechanism based on the parametric uncertainty of a critic ensemble, and (iii) ensemble-based acceleration for data-efficient RL. Evaluating CHEQ on a car racing task reveals substantially stronger data efficiency, exploration safety, and transferability to unknown scenarios than state-of-the-art adaptive hybrid RL methods.

Combining Automated Optimisation of Hyperparameters and Reward Shape

There has been significant progress in deep reinforcement learning (RL) in recent years. Nevertheless, finding suitable hyperparameter configurations and reward functions remains challenging even for experts, and performance heavily relies on these design choices. Also, most RL research is conducted on known benchmarks where knowledge about these choices already exists. However, novel practical applications often pose complex tasks for which no prior knowledge about good hyperparameters and reward functions is available, thus necessitating their derivation from scratch. Prior work has examined automatically tuning either hyperparameters or reward functions individually. We demonstrate empirically that an RL algorithm's hyperparameter configurations and reward function are often mutually dependent, meaning neither can be fully optimised without appropriate values for the other. We then propose a methodology for the combined optimisation of hyperparameters and the reward function. Furthermore, we include a variance penalty as an optimisation objective to improve the stability of learned policies. We conducted extensive experiments using Proximal Policy Optimisation and Soft Actor-Critic on four environments. Our results show that combined optimisation significantly improves over baseline performance in half of the environments and achieves competitive performance in the others, with only a minor increase in computational costs. This suggests that combined optimisation should be best practice.