Learning Representation for Bayesian Optimization with Collision-free Regularization

• URL: http://arxiv.org/abs/2203.08656v1
• Date: Wed, 16 Mar 2022 14:44:16 GMT
• Title: Learning Representation for Bayesian Optimization with Collision-free Regularization
• Authors: Fengxue Zhang, Brian Nord, Yuxin Chen
• Abstract summary: Large-scale, high-dimensional, and non-stationary datasets are common in real-world scenarios. Recent works attempt to handle such input by applying neural networks ahead of the classical Gaussian process to learn a latent representation. We show that even with proper network design, such learned representation often leads to collision in the latent space. We propose LOCo, an efficient deep Bayesian optimization framework which employs a novel regularizer to reduce the collision in the learned latent space.
• Score: 13.476552258272402
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian optimization has been challenged by datasets with large-scale, high-dimensional, and non-stationary characteristics, which are common in real-world scenarios. Recent works attempt to handle such input by applying neural networks ahead of the classical Gaussian process to learn a latent representation. We show that even with proper network design, such learned representation often leads to collision in the latent space: two points with significantly different observations collide in the learned latent space, leading to degraded optimization performance. To address this issue, we propose LOCo, an efficient deep Bayesian optimization framework which employs a novel regularizer to reduce the collision in the learned latent space and encourage the mapping from the latent space to the objective value to be Lipschitz continuous. LOCo takes in pairs of data points and penalizes those too close in the latent space compared to their target space distance. We provide a rigorous theoretical justification for LOCo by inspecting the regret of this dynamic-embedding-based Bayesian optimization algorithm, where the neural network is iteratively retrained with the regularizer. Our empirical results demonstrate the effectiveness of LOCo on several synthetic and real-world benchmark Bayesian optimization tasks.

Related papers

• Efficient Weight-Space Laplace-Gaussian Filtering and Smoothing for Sequential Deep Learning [29.328769628694484]
  Efficiently learning a sequence of related tasks, such as in continual learning, poses a significant challenge for neural nets. We address this challenge with a grounded framework for sequentially learning related tasks based on Bayesian inference.
  arXiv  Detail & Related papers  (2024-10-09T11:54:33Z)
• Efficient Second-Order Neural Network Optimization via Adaptive Trust Region Methods [0.0]
  SecondOrderAdaptive (SOAA) is a novel optimization algorithm designed to overcome limitations of traditional second-order techniques. We empirically demonstrate that SOAA achieves faster and more stable convergence compared to first-order approximations.
  arXiv  Detail & Related papers  (2024-10-03T08:23:06Z)
• Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrolling [9.20186865054847]
  Anomaly detection (AD) is increasingly recognized as a key component for ensuring the resilience of future communication systems. This work considers AD in network flows using incomplete measurements. We propose a novel block-successive convex approximation algorithm based on a regularized model-fitting objective. Inspired by Bayesian approaches, we extend the model architecture to perform online adaptation to per-flow and per-time-step statistics.
  arXiv  Detail & Related papers  (2024-09-17T19:59:57Z)
• Advancing Bayesian Optimization via Learning Correlated Latent Space [15.783344085533187]
  We propose Correlated latent space Bayesian Optimization (CoBO), which focuses on learning correlated latent spaces. Specifically, our method introduces Lipschitz regularization, loss weighting, and trust region recoordination to minimize the inherent gap around the promising areas. We demonstrate the effectiveness of our approach on several optimization tasks in discrete data, such as molecule design and arithmetic expression fitting.
  arXiv  Detail & Related papers  (2023-10-31T08:24:41Z)
• Achieving Constraints in Neural Networks: A Stochastic Augmented Lagrangian Approach [49.1574468325115]
  Regularizing Deep Neural Networks (DNNs) is essential for improving generalizability and preventing overfitting. We propose a novel approach to DNN regularization by framing the training process as a constrained optimization problem. We employ the Augmented Lagrangian (SAL) method to achieve a more flexible and efficient regularization mechanism.
  arXiv  Detail & Related papers  (2023-10-25T13:55:35Z)
• Joint inference and input optimization in equilibrium networks [68.63726855991052]
  deep equilibrium model is a class of models that foregoes traditional network depth and instead computes the output of a network by finding the fixed point of a single nonlinear layer. We show that there is a natural synergy between these two settings. We demonstrate this strategy on various tasks such as training generative models while optimizing over latent codes, training models for inverse problems like denoising and inpainting, adversarial training and gradient based meta-learning.
  arXiv  Detail & Related papers  (2021-11-25T19:59:33Z)
• Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization [98.0595480384208]
  We propose a generalization extraient spaces which converges to a stationary point. The algorithm applies not only to general $p$-normed spaces, but also to general $p$-dimensional vector spaces.
  arXiv  Detail & Related papers  (2020-10-31T21:35:42Z)
• Multi-Fidelity Bayesian Optimization via Deep Neural Networks [19.699020509495437]
  In many applications, the objective function can be evaluated at multiple fidelities to enable a trade-off between the cost and accuracy. We propose Deep Neural Network Multi-Fidelity Bayesian Optimization (DNN-MFBO) that can flexibly capture all kinds of complicated relationships between the fidelities. We show the advantages of our method in both synthetic benchmark datasets and real-world applications in engineering design.
  arXiv  Detail & Related papers  (2020-07-06T23:28:40Z)
• The Hidden Convex Optimization Landscape of Two-Layer ReLU Neural Networks: an Exact Characterization of the Optimal Solutions [51.60996023961886]
  We prove that finding all globally optimal two-layer ReLU neural networks can be performed by solving a convex optimization program with cone constraints. Our analysis is novel, characterizes all optimal solutions, and does not leverage duality-based analysis which was recently used to lift neural network training into convex spaces.
  arXiv  Detail & Related papers  (2020-06-10T15:38:30Z)
• Spatially Adaptive Inference with Stochastic Feature Sampling and Interpolation [72.40827239394565]
  We propose to compute features only at sparsely sampled locations. We then densely reconstruct the feature map with an efficient procedure. The presented network is experimentally shown to save substantial computation while maintaining accuracy over a variety of computer vision tasks.
  arXiv  Detail & Related papers  (2020-03-19T15:36:31Z)
• Learning to Hash with Graph Neural Networks for Recommender Systems [103.82479899868191]
  Graph representation learning has attracted much attention in supporting high quality candidate search at scale. Despite its effectiveness in learning embedding vectors for objects in the user-item interaction network, the computational costs to infer users' preferences in continuous embedding space are tremendous. We propose a simple yet effective discrete representation learning framework to jointly learn continuous and discrete codes.
  arXiv  Detail & Related papers  (2020-03-04T06:59:56Z)

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.