Sample-efficient Bayesian Optimisation Using Known Invariances

• URL: http://arxiv.org/abs/2410.16972v1
• Date: Tue, 22 Oct 2024 12:51:46 GMT
• Title: Sample-efficient Bayesian Optimisation Using Known Invariances
• Authors: Theodore Brown, Alexandru Cioba, Ilija Bogunovic,
• Abstract summary: We show that vanilla and constrained BO algorithms are inefficient when optimising invariant objectives. We derive a bound on the maximum information gain of these invariant kernels. We use our method to design a current drive system for a nuclear fusion reactor, finding a high-performance solution.
• Score: 56.34916328814857
• License:
• Abstract: Bayesian optimisation (BO) is a powerful framework for global optimisation of costly functions, using predictions from Gaussian process models (GPs). In this work, we apply BO to functions that exhibit invariance to a known group of transformations. We show that vanilla and constrained BO algorithms are inefficient when optimising such invariant objectives, and provide a method for incorporating group invariances into the kernel of the GP to produce invariance-aware algorithms that achieve significant improvements in sample efficiency. We derive a bound on the maximum information gain of these invariant kernels, and provide novel upper and lower bounds on the number of observations required for invariance-aware BO algorithms to achieve $\epsilon$-optimality. We demonstrate our method's improved performance on a range of synthetic invariant and quasi-invariant functions. We also apply our method in the case where only some of the invariance is incorporated into the kernel, and find that these kernels achieve similar gains in sample efficiency at significantly reduced computational cost. Finally, we use invariant BO to design a current drive system for a nuclear fusion reactor, finding a high-performance solution where non-invariant methods failed.

Related papers

• Faster WIND: Accelerating Iterative Best-of-$N$ Distillation for LLM Alignment [81.84950252537618]
  This paper reveals a unified game-theoretic connection between iterative BOND and self-play alignment. We establish a novel framework, WIN rate Dominance (WIND), with a series of efficient algorithms for regularized win rate dominance optimization.
  arXiv  Detail & Related papers  (2024-10-28T04:47:39Z)
• Variance-Reducing Couplings for Random Features [57.73648780299374]
  Random features (RFs) are a popular technique to scale up kernel methods in machine learning. We find couplings to improve RFs defined on both Euclidean and discrete input spaces. We reach surprising conclusions about the benefits and limitations of variance reduction as a paradigm.
  arXiv  Detail & Related papers  (2024-05-26T12:25:09Z)
• Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration [2.984929040246293]
  novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. New algorithms retain the ease of implementation of the classical GP-UCB, but an additional exploration step facilitates their convergence.
  arXiv  Detail & Related papers  (2024-01-30T14:16:06Z)
• Bayesian Optimization through Gaussian Cox Process Models for Spatio-temporal Data [27.922624489449017]
  We propose a novel maximum a posteriori inference of Gaussian Cox processes. We further develop a Nystr"om approximation for efficient computation.
  arXiv  Detail & Related papers  (2024-01-25T22:26:15Z)
• FAVOR#: Sharp Attention Kernel Approximations via New Classes of Positive Random Features [39.282051468586666]
  We propose parameterized, positive, non-trigonometric RFs which approximate Gaussian and softmax- Kernels. We show that our methods lead to variance reduction in practice and outperform previous methods in a kernel regression task. We also present FAVOR#, a method for self-attention approximation in Transformers.
  arXiv  Detail & Related papers  (2023-02-01T22:43:29Z)
• Extrinsic Bayesian Optimizations on Manifolds [1.3477333339913569]
  We propose an extrinsic Bayesian optimization (eBO) framework for general optimization problems on Euclid manifold. Our approach is to employ extrinsic Gaussian processes by first embedding the manifold onto some higher dimensionalean space. This leads to efficient and scalable algorithms for optimization over complex manifold.
  arXiv  Detail & Related papers  (2022-12-21T06:10:12Z)
• Generalizing Bayesian Optimization with Decision-theoretic Entropies [102.82152945324381]
  We consider a generalization of Shannon entropy from work in statistical decision theory. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures. We then show how alternative choices for the loss yield a flexible family of acquisition functions.
  arXiv  Detail & Related papers  (2022-10-04T04:43:58Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Global Optimization of Gaussian processes [52.77024349608834]
  We propose a reduced-space formulation with trained Gaussian processes trained on few data points. The approach also leads to significantly smaller and computationally cheaper sub solver for lower bounding. In total, we reduce time convergence by orders of orders of the proposed method.
  arXiv  Detail & Related papers  (2020-05-21T20:59:11Z)

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.