The Stochastic Proximal Distance Algorithm

• URL: http://arxiv.org/abs/2210.12277v4
• Date: Fri, 6 Sep 2024 03:04:51 GMT
• Title: The Stochastic Proximal Distance Algorithm
• Authors: Haoyu Jiang, Jason Xu,
• Abstract summary: We propose and analyze a class of iterative optimization methods that recover a desired constrained estimation problem as a penalty parameter. We extend recent theoretical devices to establish finite error bounds and a complete characterization of convergence rates. We validate our analysis via a thorough empirical study, also showing that unsurprisingly, the proposed method outpaces batch versions on popular learning tasks.
• Score: 5.3315823983402755
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and analyze a stochastic version of the recently proposed proximal distance algorithm, a class of iterative optimization methods that recover a desired constrained estimation problem as a penalty parameter $\rho \rightarrow \infty$. By uncovering connections to related stochastic proximal methods and interpreting the penalty parameter as the learning rate, we justify heuristics used in practical manifestations of the proximal distance method, establishing their convergence guarantees for the first time. Moreover, we extend recent theoretical devices to establish finite error bounds and a complete characterization of convergence rates regimes. We validate our analysis via a thorough empirical study, also showing that unsurprisingly, the proposed method outpaces batch versions on popular learning tasks.

Related papers

• Effectively Leveraging Momentum Terms in Stochastic Line Search Frameworks for Fast Optimization of Finite-Sum Problems [0.5156484100374059]
  We explore the relationship between recent line search approaches for deep optimization in the overparametrized regime and momentum directions. We introduce algorithmic that exploits a mix of data persistency, conjugateient type rules for the definition of the momentum parameter. The resulting algorithm is empirically shown to outperform other popular methods.
  arXiv  Detail & Related papers  (2024-11-11T16:26:33Z)
• A Unified Theory of Stochastic Proximal Point Methods without Smoothness [52.30944052987393]
  Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning. This paper presents a comprehensive analysis of a broad range of variations of the proximal point method (SPPM)
  arXiv  Detail & Related papers  (2024-05-24T21:09:19Z)
• Variance reduction techniques for stochastic proximal point algorithms [5.374800961359305]
  In this work, we propose the first unified study of variance reduction techniques for proximal point algorithms. We introduce a generic proximal-based algorithm that can be specified to give the proximal version of SVRG, SAGA, and some of their variants. Our experiments demonstrate the advantages of the proximal variance reduction methods over their gradient counterparts.
  arXiv  Detail & Related papers  (2023-08-18T05:11:50Z)
• Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization [21.022322975077653]
  Methods for solving continuous optimization problems with equality constraints have attracted attention recently. convergence guarantees have been limited to the expected value of a gradient to measure zero. New almost-sure convergence guarantees for the primals, Lagrange measures and station measures generated by a SQP algorithm are proved.
  arXiv  Detail & Related papers  (2023-08-07T16:03:40Z)
• Posterior and Computational Uncertainty in Gaussian Processes [52.26904059556759]
  Gaussian processes scale prohibitively with the size of the dataset. Many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited computation, is entirely ignored when using the approximate posterior. We develop a new class of methods that provides consistent estimation of the combined uncertainty arising from both the finite number of data observed and the finite amount of computation expended.
  arXiv  Detail & Related papers  (2022-05-30T22:16:25Z)
• A Stochastic Newton Algorithm for Distributed Convex Optimization [62.20732134991661]
  We analyze a Newton algorithm for homogeneous distributed convex optimization, where each machine can calculate gradients of the same population objective. We show that our method can reduce the number, and frequency, of required communication rounds compared to existing methods without hurting performance.
  arXiv  Detail & Related papers  (2021-10-07T17:51:10Z)
• A Boosting Approach to Reinforcement Learning [59.46285581748018]
  We study efficient algorithms for reinforcement learning in decision processes whose complexity is independent of the number of states. We give an efficient algorithm that is capable of improving the accuracy of such weak learning methods.
  arXiv  Detail & Related papers  (2021-08-22T16:00:45Z)
• Minibatch and Momentum Model-based Methods for Stochastic Non-smooth Non-convex Optimization [3.4809730725241597]
  We make two important extensions to model-based methods. First, we propose a new minibatch which takes a set of samples to approximate the model function in each iteration. Second, by the success of momentum techniques we propose a new convex-based model.
  arXiv  Detail & Related papers  (2021-06-06T05:31:57Z)
• Proximal Gradient Temporal Difference Learning: Stable Reinforcement Learning with Polynomial Sample Complexity [40.73281056650241]
  We introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true gradient temporal difference learning algorithms. We show how gradient TD reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function.
  arXiv  Detail & Related papers  (2020-06-06T21:04:21Z)
• A Distributional Analysis of Sampling-Based Reinforcement Learning Algorithms [67.67377846416106]
  We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We show that value-based methods such as TD($lambda$) and $Q$-Learning have update rules which are contractive in the space of distributions of functions.
  arXiv  Detail & Related papers  (2020-03-27T05:13:29Z)
• Is Temporal Difference Learning Optimal? An Instance-Dependent Analysis [102.29671176698373]
  We address the problem of policy evaluation in discounted decision processes, and provide Markov-dependent guarantees on the $ell_infty$error under a generative model. We establish both and non-asymptotic versions of local minimax lower bounds for policy evaluation, thereby providing an instance-dependent baseline by which to compare algorithms.
  arXiv  Detail & Related papers  (2020-03-16T17:15:28Z)

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.