Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space

• URL: http://arxiv.org/abs/2407.11917v3
• Date: Sun, 3 Nov 2024 13:37:04 GMT
• Title: Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space
• Authors: Tigran Ramazyan, Mikhail Hushchyn, Denis Derkach,
• Abstract summary: optimisation of black-box simulators is challenging for simulators and higher dimensions. We use a deep generative surrogate approach to model the black box response for the entire parameter space. We then leverage this knowledge to estimate the proposed uncertainty based on the Wasserstein distance.
• Score: 0.28675177318965045
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new uncertainty estimator for gradient-free optimisation of black-box simulators using deep generative surrogate models. Optimisation of these simulators is especially challenging for stochastic simulators and higher dimensions. To address these issues, we utilise a deep generative surrogate approach to model the black box response for the entire parameter space. We then leverage this knowledge to estimate the proposed uncertainty based on the Wasserstein distance - the Wasserstein uncertainty. This approach is employed in a posterior agnostic gradient-free optimisation algorithm that minimises regret over the entire parameter space. A series of tests were conducted to demonstrate that our method is more robust to the shape of both the black box function and the stochastic response of the black box than state-of-the-art methods, such as efficient global optimisation with a deep Gaussian process surrogate.

Related papers

• Covariance-Adaptive Sequential Black-box Optimization for Diffusion Targeted Generation [60.41803046775034]
  We show how to perform user-preferred targeted generation via diffusion models with only black-box target scores of users. Experiments on both numerical test problems and target-guided 3D-molecule generation tasks show the superior performance of our method in achieving better target scores.
  arXiv  Detail & Related papers  (2024-06-02T17:26:27Z)
• Latent Energy-Based Odyssey: Black-Box Optimization via Expanded Exploration in the Energy-Based Latent Space [65.44449711359724]
  High-dimensional and highly-multimodal input design space of black-box function pose inherent challenges for existing methods. We consider finding a latent space that serves as a compressed yet accurate representation of the design-value joint space. We propose Noise-intensified Telescoping density-Ratio Estimation scheme for variational learning of an accurate latent space model.
  arXiv  Detail & Related papers  (2024-05-27T00:11:53Z)
• 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)
• Multi-fidelity Constrained Optimization for Stochastic Black Box Simulators [1.6385815610837167]
  We introduce the algorithm Scout-Nd (Stochastic Constrained Optimization for N dimensions) to tackle the issues mentioned earlier. Scout-Nd efficiently estimates the gradient, reduces the noise of the estimator gradient, and applies multi-fidelity schemes to further reduce computational effort. We validate our approach on standard benchmarks, demonstrating its effectiveness in optimizing parameters highlighting better performance compared to existing methods.
  arXiv  Detail & Related papers  (2023-11-25T23:36:38Z)
• Stochastic Marginal Likelihood Gradients using Neural Tangent Kernels [78.6096486885658]
  We introduce lower bounds to the linearized Laplace approximation of the marginal likelihood. These bounds are amenable togradient-based optimization and allow to trade off estimation accuracy against computational complexity.
  arXiv  Detail & Related papers  (2023-06-06T19:02:57Z)
• Surrogate modeling for Bayesian optimization beyond a single Gaussian process [62.294228304646516]
  We propose a novel Bayesian surrogate model to balance exploration with exploitation of the search space. To endow function sampling with scalability, random feature-based kernel approximation is leveraged per GP model. To further establish convergence of the proposed EGP-TS to the global optimum, analysis is conducted based on the notion of Bayesian regret.
  arXiv  Detail & Related papers  (2022-05-27T16:43:10Z)
• Bayesian Optimisation for Constrained Problems [0.0]
  We propose a novel variant of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the new algorithm with four other state-of-the-art constrained Bayesian optimisation algorithms and demonstrate its superior performance.
  arXiv  Detail & Related papers  (2021-05-27T15:43:09Z)
• Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework [100.36569795440889]
  This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information. We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
  arXiv  Detail & Related papers  (2020-12-21T17:29:58Z)
• Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces [63.22864716473051]
  We propose a novel BO algorithm which expands (and shifts) the search space over iterations. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates.
  arXiv  Detail & Related papers  (2020-09-05T14:24:40Z)
• Upper Trust Bound Feasibility Criterion for Mixed Constrained Bayesian Optimization with Application to Aircraft Design [41.74498230885008]
  We adapt the so-called super effcient global optimization algorithm to solve more accurately mixed constrained problems. We show the good potential of the approach on a set of numerical experiments.
  arXiv  Detail & Related papers  (2020-05-11T12:59:09Z)
• Black-Box Optimization with Local Generative Surrogates [6.04055755718349]
  In fields such as physics and engineering, many processes are modeled with non-differentiable simulators with intractable likelihoods. We introduce the use of deep generative models to approximate the simulator in local neighborhoods of the parameter space. In cases where the dependence of the simulator on the parameter space is constrained to a low dimensional submanifold, we observe that our method attains minima faster than baseline methods.
  arXiv  Detail & Related papers  (2020-02-11T19:02:57Z)

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.