Towards safe Bayesian optimization with Wiener kernel regression

• URL: http://arxiv.org/abs/2411.02253v3
• Date: Mon, 14 Apr 2025 11:36:12 GMT
• Title: Towards safe Bayesian optimization with Wiener kernel regression
• Authors: Oleksii Molodchyk, Johannes Teutsch, Timm Faulwasser,
• Abstract summary: We present a novel error bound based on the recently proposed Wiener kernel regression.<n>We prove that under rather mild assumptions, the proposed error bound is tighter than bounds previously documented in the literature.<n>We draw upon a numerical example to demonstrate the efficacy of the proposed error bound in safe BO.
• Score: 0.6554326244334868
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian Optimization (BO) is a data-driven strategy for minimizing/maximizing black-box functions based on probabilistic surrogate models. In the presence of safety constraints, the performance of BO crucially relies on tight probabilistic error bounds related to the uncertainty surrounding the surrogate model. For the case of Gaussian Process surrogates and Gaussian measurement noise, we present a novel error bound based on the recently proposed Wiener kernel regression. We prove that under rather mild assumptions, the proposed error bound is tighter than bounds previously documented in the literature, leading to enlarged safety regions. We draw upon a numerical example to demonstrate the efficacy of the proposed error bound in safe BO.

Related papers

• Continuous Bayesian Model Selection for Multivariate Causal Discovery [22.945274948173182]
  Current causal discovery approaches require restrictive model assumptions or assume access to interventional data to ensure structure identifiability. Recent work has shown that Bayesian model selection can greatly improve accuracy by exchanging restrictive modelling for more flexible assumptions. We demonstrate the competitiveness of our approach on both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2024-11-15T12:55:05Z)
• Information-Theoretic Safe Bayesian Optimization [59.758009422067005]
  We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an unknown (safety) constraint. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. We propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate.
  arXiv  Detail & Related papers  (2024-02-23T14:31:10Z)
• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability [50.44439018155837]
  We propose to include a calibration term directly into the training objective of the neural model. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference.
  arXiv  Detail & Related papers  (2023-10-20T10:20:45Z)
• Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels [57.46832672991433]
  We propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS) We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We develop an expectation-propagation expectation-maximization algorithm for efficient posterior inference and function estimation.
  arXiv  Detail & Related papers  (2023-10-09T03:55:09Z)
• Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes [23.87733307119697]
  We introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes. NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior. We demonstrate that the bias introduced by our method can be controlled by multiplying the divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm.
  arXiv  Detail & Related papers  (2023-09-22T06:56:35Z)
• Model-based Causal Bayesian Optimization [78.120734120667]
  We propose model-based causal Bayesian optimization (MCBO) MCBO learns a full system model instead of only modeling intervention-reward pairs. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form.
  arXiv  Detail & Related papers  (2022-11-18T14:28:21Z)
• Risk-averse Heteroscedastic Bayesian Optimization [45.12421486836736]
  We propose a novel risk-averse heteroscedastic Bayesian optimization algorithm (RAHBO) RAHBO aims to identify a solution with high return and low noise variance, while learning the noise distribution on the fly. We provide a robust rule to report the final decision point for applications where only a single solution must be identified.
  arXiv  Detail & Related papers  (2021-11-05T17:38:34Z)
• Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications [71.23286211775084]
  We introduce robust Gaussian process uniform error bounds in settings with unknown hyper parameters. Our approach computes a confidence region in the space of hyper parameters, which enables us to obtain a probabilistic upper bound for the model error. Experiments show that the bound performs significantly better than vanilla and fully Bayesian processes.
  arXiv  Detail & Related papers  (2021-09-06T17:10:01Z)

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.