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Abstract:Safe Bayesian optimization (BO) algorithms promise to find optimal control policies without knowing the system dynamics while at the same time guaranteeing safety with high probability. In exchange for those guarantees, popular algorithms require a smoothness assumption: a known upper bound on a norm in a reproducing kernel Hilbert space (RKHS). The RKHS is a potentially infinite-dimensional space, and it is unclear how to, in practice, obtain an upper bound of an unknown function in its corresponding RKHS. In response, we propose an algorithm that estimates an upper bound on the RKHS norm of an unknown function from data and investigate its theoretical properties. Moreover, akin to Lipschitz-based methods, we treat the RKHS norm as a local rather than a global object, and thus reduce conservatism. Integrating the RKHS norm estimation and the local interpretation of the RKHS norm into a safe BO algorithm yields PACSBO, an algorithm for probably approximately correct safe Bayesian optimization, for which we provide numerical and hardware experiments that demonstrate its applicability and benefits over popular safe BO algorithms.

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Abstract:When deploying machine learning algorithms in the real world, guaranteeing safety is an essential asset. Existing safe learning approaches typically consider continuous variables, i.e., regression tasks. However, in practice, robotic systems are also subject to discrete, external environmental changes, e.g., having to carry objects of certain weights or operating on frozen, wet, or dry surfaces. Such influences can be modeled as discrete context variables. In the existing literature, such contexts are, if considered, mostly assumed to be known. In this work, we drop this assumption and show how we can perform safe learning when we cannot directly measure the context variables. To achieve this, we derive frequentist guarantees for multi-class classification, allowing us to estimate the current context from measurements. Further, we propose an approach for identifying contexts through experiments. We discuss under which conditions we can retain theoretical guarantees and demonstrate the applicability of our algorithm on a Furuta pendulum with camera measurements of different weights that serve as contexts.

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Abstract:Envisioned application areas for reinforcement learning (RL) include autonomous driving, precision agriculture, and finance, which all require RL agents to make decisions in the real world. A significant challenge hindering the adoption of RL methods in these domains is the non-robustness of conventional algorithms. In this paper, we argue that a fundamental issue contributing to this lack of robustness lies in the focus on the expected value of the return as the sole "correct" optimization objective. The expected value is the average over the statistical ensemble of infinitely many trajectories. For non-ergodic returns, this average differs from the average over a single but infinitely long trajectory. Consequently, optimizing the expected value can lead to policies that yield exceptionally high returns with probability zero but almost surely result in catastrophic outcomes. This problem can be circumvented by transforming the time series of collected returns into one with ergodic increments. This transformation enables learning robust policies by optimizing the long-term return for individual agents rather than the average across infinitely many trajectories. We propose an algorithm for learning ergodicity transformations from data and demonstrate its effectiveness in an instructive, non-ergodic environment and on standard RL benchmarks.

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Abstract:Safety is an essential asset when learning control policies for physical systems, as violating safety constraints during training can lead to expensive hardware damage. In response to this need, the field of safe learning has emerged with algorithms that can provide probabilistic safety guarantees without knowledge of the underlying system dynamics. Those algorithms often rely on Gaussian process inference. Unfortunately, Gaussian process inference scales cubically with the number of data points, limiting applicability to high-dimensional and embedded systems. In this paper, we propose a safe learning algorithm that provides probabilistic safety guarantees but leverages the Nadaraya-Watson estimator instead of Gaussian processes. For the Nadaraya-Watson estimator, we can reach logarithmic scaling with the number of data points. We provide theoretical guarantees for the estimates, embed them into a safe learning algorithm, and show numerical experiments on a simulated seven-degrees-of-freedom robot manipulator.

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Authors:Sebastian Weichwald, Søren Wengel Mogensen, Tabitha Edith Lee, Dominik Baumann, Oliver Kroemer, Isabelle Guyon, Sebastian Trimpe, Jonas Peters, Niklas Pfister

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Abstract:Questions in causality, control, and reinforcement learning go beyond the classical machine learning task of prediction under i.i.d. observations. Instead, these fields consider the problem of learning how to actively perturb a system to achieve a certain effect on a response variable. Arguably, they have complementary views on the problem: In control, one usually aims to first identify the system by excitation strategies to then apply model-based design techniques to control the system. In (non-model-based) reinforcement learning, one directly optimizes a reward. In causality, one focus is on identifiability of causal structure. We believe that combining the different views might create synergies and this competition is meant as a first step toward such synergies. The participants had access to observational and (offline) interventional data generated by dynamical systems. Track CHEM considers an open-loop problem in which a single impulse at the beginning of the dynamics can be set, while Track ROBO considers a closed-loop problem in which control variables can be set at each time step. The goal in both tracks is to infer controls that drive the system to a desired state. Code is open-sourced ( https://github.com/LearningByDoingCompetition/learningbydoing-comp ) to reproduce the winning solutions of the competition and to facilitate trying out new methods on the competition tasks.

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Authors:Bhavya Sukhija, Matteo Turchetta, David Lindner, Andreas Krause, Sebastian Trimpe, Dominik Baumann

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Abstract:Learning optimal control policies directly on physical systems is challenging since even a single failure can lead to costly hardware damage. Most existing learning methods that guarantee safety, i.e., no failures, during exploration are limited to local optima. A notable exception is the GoSafe algorithm, which, unfortunately, cannot handle high-dimensional systems and hence cannot be applied to most real-world dynamical systems. This work proposes GoSafeOpt as the first algorithm that can safely discover globally optimal policies for complex systems while giving safety and optimality guarantees. Our experiments on a robot arm that would be prohibitive for GoSafe demonstrate that GoSafeOpt safely finds remarkably better policies than competing safe learning methods for high-dimensional domains.

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Abstract:When learning policies for robotic systems from data, safety is a major concern, as violation of safety constraints may cause hardware damage. SafeOpt is an efficient Bayesian optimization (BO) algorithm that can learn policies while guaranteeing safety with high probability. However, its search space is limited to an initially given safe region. We extend this method by exploring outside the initial safe area while still guaranteeing safety with high probability. This is achieved by learning a set of initial conditions from which we can recover safely using a learned backup controller in case of a potential failure. We derive conditions for guaranteed convergence to the global optimum and validate GoSafe in hardware experiments.

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Authors:Alonso Marco, Dominik Baumann, Majid Khadiv, Philipp Hennig, Ludovic Righetti, Sebastian Trimpe

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Abstract:In the past decade, numerous machine learning algorithms have been shown to successfully learn optimal policies to control real robotic systems. However, it is not rare to encounter failing behaviors as the learning loop progresses. Specifically, in robot applications where failing is undesired but not catastrophic, many algorithms struggle with leveraging data obtained from failures. This is usually caused by (i) the failed experiment ending prematurely, or (ii) the acquired data being scarce or corrupted. Both complicate the design of proper reward functions to penalize failures. In this paper, we propose a framework that addresses those issues. We consider failing behaviors as those that violate a constraint and address the problem of "learning with crash constraints", where no data is obtained upon constraint violation. The no-data case is addressed by a novel GP model (GPCR) for the constraint that combines discrete events (failure/success) with continuous observations (only obtained upon success). We demonstrate the effectiveness of our framework on simulated benchmarks and on a real jumping quadruped, where the constraint boundary is unknown a priori. Experimental data is collected, by means of constrained Bayesian optimization, directly on the real robot. Our results outperform manual tuning and GPCR proves useful on estimating the constraint boundary.

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Abstract:We present a framework for model-free learning of event-triggered control strategies. Event-triggered methods aim to achieve high control performance while only closing the feedback loop when needed. This enables resource savings, e.g., network bandwidth if control commands are sent via communication networks, as in networked control systems. Event-triggered controllers consist of a communication policy, determining when to communicate, and a control policy, deciding what to communicate. It is essential to jointly optimize the two policies since individual optimization does not necessarily yield the overall optimal solution. To address this need for joint optimization, we propose a novel algorithm based on hierarchical reinforcement learning. The resulting algorithm is shown to accomplish high-performance control in line with resource savings and scales seamlessly to nonlinear and high-dimensional systems. The method's applicability to real-world scenarios is demonstrated through experiments on a six degrees of freedom real-time controlled manipulator. Further, we propose an approach towards evaluating the stability of the learned neural network policies.

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Abstract:We present a method for automatically identifying the causal structure of a dynamical control system. Through a suitable experiment design and subsequent causal analysis, the method reveals, which state and input variables of the system have a causal influence on each other. The experiment design builds on the concept of controllability, which provides a systematic way to compute input trajectories that steer the system to specific regions in its state space. For the causal analysis, we leverage powerful techniques from causal inference and extend them to control systems. Further, we derive conditions that guarantee discovery of the true causal structure of the system and show that the obtained knowledge of the causal structure reduces the complexity of model learning and yields improved generalization capabilities. Experiments on a robot arm demonstrate reliable causal identification from real-world data and extrapolation to regions outside the training domain.

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