Safe exploration in reproducing kernel Hilbert spaces

• URL: http://arxiv.org/abs/2503.10352v1
• Date: Thu, 13 Mar 2025 13:28:54 GMT
• Title: Safe exploration in reproducing kernel Hilbert spaces
• Authors: Abdullah Tokmak, Kiran G. Krishnan, Thomas B. Schön, Dominik Baumann,
• Abstract summary: We propose a safe BO algorithm capable of estimating the RKHS norm from data.<n>We apply our algorithm to safely optimize reinforcement learning policies on physics simulators and on a real inverted pendulum.
• Score: 9.600218079563291
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Popular safe Bayesian optimization (BO) algorithms learn control policies for safety-critical systems in unknown environments. However, most algorithms make a smoothness assumption, which is encoded by a known bounded norm in a reproducing kernel Hilbert space (RKHS). The RKHS is a potentially infinite-dimensional space, and it remains unclear how to reliably obtain the RKHS norm of an unknown function. In this work, we propose a safe BO algorithm capable of estimating the RKHS norm from data. We provide statistical guarantees on the RKHS norm estimation, integrate the estimated RKHS norm into existing confidence intervals and show that we retain theoretical guarantees, and prove safety of the resulting safe BO algorithm. We apply our algorithm to safely optimize reinforcement learning policies on physics simulators and on a real inverted pendulum, demonstrating improved performance, safety, and scalability compared to the state-of-the-art.

Related papers

• PACSBO: Probably approximately correct safe Bayesian optimization [10.487548576958421]
  We propose an algorithm that estimates an upper bound on the RKHS norm of an unknown function from data. 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.
  arXiv  Detail & Related papers  (2024-09-02T10:50:34Z)
• On Safety in Safe Bayesian Optimization [5.9045432488022485]
  We investigate three safety-related issues of the popular class of SafeOpt-type algorithms. First, these algorithms critically rely on frequentist bounds uncertainty for Gaussian Process (GP) regression. Second, we identify assuming an upper bound on the reproducing kernel Hilbert space (RKHS) norm of the target function. Third, SafeOpt and derived algorithms rely on a discrete search space, making them difficult to apply to higher-dimensional problems.
  arXiv  Detail & Related papers  (2024-03-19T17:50:32Z)
• Leveraging Approximate Model-based Shielding for Probabilistic Safety Guarantees in Continuous Environments [63.053364805943026]
  We extend the approximate model-based shielding framework to the continuous setting. In particular we use Safety Gym as our test-bed, allowing for a more direct comparison of AMBS with popular constrained RL algorithms.
  arXiv  Detail & Related papers  (2024-02-01T17:55:08Z)
• Safe Exploration in Reinforcement Learning: A Generalized Formulation and Algorithms [8.789204441461678]
  We present a solution of the safe exploration (GSE) problem in the form of a meta-algorithm for safe exploration, MASE. Our proposed algorithm achieves better performance than state-of-the-art algorithms on grid-world and Safety Gym benchmarks.
  arXiv  Detail & Related papers  (2023-10-05T00:47:09Z)
• Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learning [72.97229770329214]
  We introduce a general approach for seeking high dimensional non-linear optimization problems in which maintaining safety during learning is crucial. Our approach called LBSGD is based on applying a logarithmic barrier approximation with a carefully chosen step size. We demonstrate the effectiveness of our approach on minimizing violation in policy tasks in safe reinforcement learning.
  arXiv  Detail & Related papers  (2022-07-21T11:14:47Z)
• Safe Reinforcement Learning via Confidence-Based Filters [78.39359694273575]
  We develop a control-theoretic approach for certifying state safety constraints for nominal policies learned via standard reinforcement learning techniques. We provide formal safety guarantees, and empirically demonstrate the effectiveness of our approach.
  arXiv  Detail & Related papers  (2022-07-04T11:43:23Z)
• Meta-Learning Hypothesis Spaces for Sequential Decision-making [79.73213540203389]
  We propose to meta-learn a kernel from offline data (Meta-KeL) Under mild conditions, we guarantee that our estimated RKHS yields valid confidence sets. We also empirically evaluate the effectiveness of our approach on a Bayesian optimization task.
  arXiv  Detail & Related papers  (2022-02-01T17:46:51Z)
• Safe Policy Optimization with Local Generalized Linear Function Approximations [17.84511819022308]
  Existing safe exploration methods guaranteed safety under the assumption of regularity. We propose a novel algorithm, SPO-LF, that optimize an agent's policy while learning the relation between a locally available feature obtained by sensors and environmental reward/safety. We experimentally show that our algorithm is 1) more efficient in terms of sample complexity and computational cost and 2) more applicable to large-scale problems than previous safe RL methods with theoretical guarantees.
  arXiv  Detail & Related papers  (2021-11-09T00:47:50Z)
• Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems [81.7983463275447]
  Learning-based control algorithms require data collection with abundant supervision for training. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained optimal control with dynamics learning and feedback control.
  arXiv  Detail & Related papers  (2020-05-09T05:57:43Z)
• Representation of Reinforcement Learning Policies in Reproducing Kernel Hilbert Spaces [72.5149277196468]
  This framework involves finding a low-dimensional embedding of the policy on a kernel Hilbert space (RKHS) We derive strong theoretical guarantees on the expected return of the reconstructed policy. The results confirm that the policies can be robustly embedded in a low-dimensional space while the embedded policy incurs almost no decrease in return.
  arXiv  Detail & Related papers  (2020-02-07T15:57:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.