Optimum-statistical Collaboration Towards General and Efficient Black-box Optimization

• URL: http://arxiv.org/abs/2106.09215v5
• Date: Wed, 31 May 2023 05:07:00 GMT
• Title: Optimum-statistical Collaboration Towards General and Efficient Black-box Optimization
• Authors: Wenjie Li, Chi-Hua Wang, Guang Cheng, Qifan Song
• Abstract summary: We introduce an algorithm framework of managing the interaction between optimization error flux and statistical error flux evolving in the optimization process. Our framework and its analysis can be applied to a large family of functions and partitions that satisfy different local smoothness assumptions. In theory, we prove the algorithm enjoys rate-optimal regret bounds under different local smoothness assumptions.
• Score: 23.359363844344408
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we make the key delineation on the roles of resolution and statistical uncertainty in hierarchical bandits-based black-box optimization algorithms, guiding a more general analysis and a more efficient algorithm design. We introduce the \textit{optimum-statistical collaboration}, an algorithm framework of managing the interaction between optimization error flux and statistical error flux evolving in the optimization process. We provide a general analysis of this framework without specifying the forms of statistical error and uncertainty quantifier. Our framework and its analysis, due to their generality, can be applied to a large family of functions and partitions that satisfy different local smoothness assumptions and have different numbers of local optimums, which is much richer than the class of functions studied in prior works. Our framework also inspires us to propose a better measure of the statistical uncertainty and consequently a variance-adaptive algorithm \texttt{VHCT}. In theory, we prove the algorithm enjoys rate-optimal regret bounds under different local smoothness assumptions; in experiments, we show the algorithm outperforms prior efforts in different settings.

Related papers

• Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems [61.580419063416734]
  A recent stream of structured learning approaches has improved the practical state of the art for a range of optimization problems. The key idea is to exploit the statistical distribution over instances instead of dealing with instances separately. In this article, we investigate methods that smooth the risk by perturbing the policy, which eases optimization and improves the generalization error.
  arXiv  Detail & Related papers  (2024-07-24T12:00:30Z)
• Beyond Single-Model Views for Deep Learning: Optimization versus Generalizability of Stochastic Optimization Algorithms [13.134564730161983]
  This paper adopts a novel approach to deep learning optimization, focusing on gradient descent (SGD) and its variants. We show that SGD and its variants demonstrate performance on par with flat-minimas like SAM, albeit with half the gradient evaluations. Our study uncovers several key findings regarding the relationship between training loss and hold-out accuracy, as well as the comparable performance of SGD and noise-enabled variants.
  arXiv  Detail & Related papers  (2024-03-01T14:55:22Z)
• Parameter-Free Algorithms for Performative Regret Minimization under Decision-Dependent Distributions [15.396561118589577]
  performative risk minimization is a formulation of optimization under decision-dependent distributions. Our algorithms significantly improve upon existing Lipschitz constant distribution parameter-based methods. We provide experimental results that demonstrate the numerical superiority of our algorithms over the existing method and other black-box optimistic optimization methods.
  arXiv  Detail & Related papers  (2024-02-23T08:36:28Z)
• Explainable Benchmarking for Iterative Optimization Heuristics [0.8192907805418583]
  We introduce the IOH-Xplainer software framework, for analyzing and understanding the performance of various optimization algorithms. We examine the impact of different algorithmic components and configurations, offering insights into their performance across diverse scenarios.
  arXiv  Detail & Related papers  (2024-01-31T14:02:26Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• A unified surrogate-based scheme for black-box and preference-based optimization [2.561649173827544]
  We show that black-box and preference-based optimization problems are closely related and can be solved using the same family of approaches. We propose the generalized Metric Response Surface (gMRS) algorithm, an optimization scheme that is a generalization of the popular MSRS framework.
  arXiv  Detail & Related papers  (2022-02-03T08:47:54Z)
• Amortized Implicit Differentiation for Stochastic Bilevel Optimization [53.12363770169761]
  We study a class of algorithms for solving bilevel optimization problems in both deterministic and deterministic settings. We exploit a warm-start strategy to amortize the estimation of the exact gradient. By using this framework, our analysis shows these algorithms to match the computational complexity of methods that have access to an unbiased estimate of the gradient.
  arXiv  Detail & Related papers  (2021-11-29T15:10:09Z)
• Outlier-Robust Sparse Estimation via Non-Convex Optimization [73.18654719887205]
  We explore the connection between high-dimensional statistics and non-robust optimization in the presence of sparsity constraints. We develop novel and simple optimization formulations for these problems. As a corollary, we obtain that any first-order method that efficiently converges to station yields an efficient algorithm for these tasks.
  arXiv  Detail & Related papers  (2021-09-23T17:38:24Z)
• Bilevel Optimization: Convergence Analysis and Enhanced Design [63.64636047748605]
  Bilevel optimization is a tool for many machine learning problems. We propose a novel stoc-efficientgradient estimator named stoc-BiO.
  arXiv  Detail & Related papers  (2020-10-15T18:09:48Z)
• Stochastic batch size for adaptive regularization in deep network optimization [63.68104397173262]
  We propose a first-order optimization algorithm incorporating adaptive regularization applicable to machine learning problems in deep learning framework. We empirically demonstrate the effectiveness of our algorithm using an image classification task based on conventional network models applied to commonly used benchmark datasets.
  arXiv  Detail & Related papers  (2020-04-14T07:54:53Z)

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.