OptEx: Expediting First-Order Optimization with Approximately Parallelized Iterations

• URL: http://arxiv.org/abs/2402.11427v2
• Date: Tue, 29 Oct 2024 04:20:44 GMT
• Title: OptEx: Expediting First-Order Optimization with Approximately Parallelized Iterations
• Authors: Yao Shu, Jiongfeng Fang, Ying Tiffany He, Fei Richard Yu,
• Abstract summary: We introduce first-order optimization expedited with approximately parallelized iterations (OptEx) OptEx is the first framework that enhances the efficiency of FOO by leveraging parallel computing to mitigate its iterative bottleneck. We provide theoretical guarantees for the reliability of our kernelized gradient estimation and the complexity of SGD-based OptEx.
• Score: 12.696136981847438
• License:
• Abstract: First-order optimization (FOO) algorithms are pivotal in numerous computational domains such as machine learning and signal denoising. However, their application to complex tasks like neural network training often entails significant inefficiencies due to the need for many sequential iterations for convergence. In response, we introduce first-order optimization expedited with approximately parallelized iterations (OptEx), the first framework that enhances the efficiency of FOO by leveraging parallel computing to mitigate its iterative bottleneck. OptEx employs kernelized gradient estimation to make use of gradient history for future gradient prediction, enabling parallelization of iterations -- a strategy once considered impractical because of the inherent iterative dependency in FOO. We provide theoretical guarantees for the reliability of our kernelized gradient estimation and the iteration complexity of SGD-based OptEx, confirming that estimation errors diminish to zero as historical gradients accumulate and that SGD-based OptEx enjoys an effective acceleration rate of $\Omega(\sqrt{N})$ over standard SGD given parallelism of N. We also use extensive empirical studies, including synthetic functions, reinforcement learning tasks, and neural network training across various datasets, to underscore the substantial efficiency improvements achieved by OptEx.

Related papers

• Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling [0.0]
  This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA) Numerical experiments demonstrate that our method is a competitive general-purpose solver, achieving performance comparable to iSCO and learning-based solvers.
  arXiv  Detail & Related papers  (2024-09-02T12:55:27Z)
• ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport [3.0237149871998095]
  We present a new approach to accurately and efficiently estimating optimal transportation plan. It is called ExpectileRegularised Neural Transport Optimal (ENOT) ENOT enforces binding conditions on the learning process of dual potentials.
  arXiv  Detail & Related papers  (2024-03-06T15:15:42Z)
• Posterior Sampling with Delayed Feedback for Reinforcement Learning with Linear Function Approximation [62.969796245827006]
  Delayed-PSVI is an optimistic value-based algorithm that explores the value function space via noise perturbation with posterior sampling. We show our algorithm achieves $widetildeO(sqrtd3H3 T + d2H2 E[tau]$ worst-case regret in the presence of unknown delays. We incorporate a gradient-based approximate sampling scheme via Langevin dynamics for Delayed-LPSVI.
  arXiv  Detail & Related papers  (2023-10-29T06:12:43Z)
• Federated Conditional Stochastic Optimization [110.513884892319]
  Conditional optimization has found in a wide range of machine learning tasks, such as in-variant learning tasks, AUPRC, andAML. This paper proposes algorithms for distributed federated learning.
  arXiv  Detail & Related papers  (2023-10-04T01:47:37Z)
• Ordering for Non-Replacement SGD [7.11967773739707]
  We seek to find an ordering that can improve the convergence rates for the non-replacement form of the algorithm. We develop optimal orderings for constant and decreasing step sizes for strongly convex and convex functions. In addition, we are able to combine the ordering with mini-batch and further apply it to more complex neural networks.
  arXiv  Detail & Related papers  (2023-06-28T00:46:58Z)
• End-to-End Meta-Bayesian Optimisation with Transformer Neural Processes [52.818579746354665]
  This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data.
  arXiv  Detail & Related papers  (2023-05-25T10:58:46Z)
• Stochastic Unrolled Federated Learning [85.6993263983062]
  We introduce UnRolled Federated learning (SURF), a method that expands algorithm unrolling to federated learning. Our proposed method tackles two challenges of this expansion, namely the need to feed whole datasets to the unrolleds and the decentralized nature of federated learning.
  arXiv  Detail & Related papers  (2023-05-24T17:26:22Z)
• Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learning [45.78238792836363]
  We present a single-loop algorithm named SLEDGE (Single-Loop-E Gradient Estimator) for periodic convergence. Unlike existing methods, SLEDGE has the advantage of versatility; (ii) second-order optimal, (ii) in the PL region, and (iii) smaller complexity under less of data.
  arXiv  Detail & Related papers  (2022-09-01T11:05:26Z)
• 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)
• Efficient Learning of Generative Models via Finite-Difference Score Matching [111.55998083406134]
  We present a generic strategy to efficiently approximate any-order directional derivative with finite difference. Our approximation only involves function evaluations, which can be executed in parallel, and no gradient computations.
  arXiv  Detail & Related papers  (2020-07-07T10:05:01Z)
• Towards Understanding Label Smoothing [36.54164997035046]
  Label smoothing regularization (LSR) has a great success in deep neural networks by training algorithms. We show that an appropriate LSR can help to speed up convergence by reducing the variance. We propose a simple yet effective strategy, namely Two-Stage LAbel smoothing algorithm (TSLA)
  arXiv  Detail & Related papers  (2020-06-20T20:36:17Z)

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.