Online Nonconvex Bilevel Optimization with Bregman Divergences

• URL: http://arxiv.org/abs/2409.10470v1
• Date: Mon, 16 Sep 2024 17:01:27 GMT
• Title: Online Nonconvex Bilevel Optimization with Bregman Divergences
• Authors: Jason Bohne, David Rosenberg, Gary Kazantsev, Pawel Polak,
• Abstract summary: We introduce an online bilevel (SOB) method for updating outer-level variables using an average of recent variance rates. This approach is superior to the setting offline bilevel (OBO) as rates of hyperlevel benchmarks highlight the superior performance and efficiency.
• Score: 3.237380113935023
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bilevel optimization methods are increasingly relevant within machine learning, especially for tasks such as hyperparameter optimization and meta-learning. Compared to the offline setting, online bilevel optimization (OBO) offers a more dynamic framework by accommodating time-varying functions and sequentially arriving data. This study addresses the online nonconvex-strongly convex bilevel optimization problem. In deterministic settings, we introduce a novel online Bregman bilevel optimizer (OBBO) that utilizes adaptive Bregman divergences. We demonstrate that OBBO enhances the known sublinear rates for bilevel local regret through a novel hypergradient error decomposition that adapts to the underlying geometry of the problem. In stochastic contexts, we introduce the first stochastic online bilevel optimizer (SOBBO), which employs a window averaging method for updating outer-level variables using a weighted average of recent stochastic approximations of hypergradients. This approach not only achieves sublinear rates of bilevel local regret but also serves as an effective variance reduction strategy, obviating the need for additional stochastic gradient samples at each timestep. Experiments on online hyperparameter optimization and online meta-learning highlight the superior performance, efficiency, and adaptability of our Bregman-based algorithms compared to established online and offline bilevel benchmarks.

Related papers

• BILBO: BILevel Bayesian Optimization [36.88993287853141]
  Bilevel optimization is characterized by a two-level structure, where the upper-level problem is constrained by optimal lower-level solutions. We present BILevel Bayesian Optimization (BILBO), a novel algorithm for general bilevel problems with blackbox functions.
  arXiv  Detail & Related papers  (2025-02-04T08:57:47Z)
• Provably Faster Algorithms for Bilevel Optimization via Without-Replacement Sampling [96.47086913559289]
  gradient-based algorithms are widely used in bilevel optimization. We introduce a without-replacement sampling based algorithm which achieves a faster convergence rate. We validate our algorithms over both synthetic and real-world applications.
  arXiv  Detail & Related papers  (2024-11-07T17:05:31Z)
• Gradient-Variation Online Learning under Generalized Smoothness [56.38427425920781]
  gradient-variation online learning aims to achieve regret guarantees that scale with variations in gradients of online functions. Recent efforts in neural network optimization suggest a generalized smoothness condition, allowing smoothness to correlate with gradient norms. We provide the applications for fast-rate convergence in games and extended adversarial optimization.
  arXiv  Detail & Related papers  (2024-08-17T02:22:08Z)
• Bilevel Optimization under Unbounded Smoothness: A New Algorithm and Convergence Analysis [17.596465452814883]
  Current bilevel optimization algorithms assume that the iterations of the upper-level function is unbounded smooth. Recent studies reveal that certain neural networks exhibit such unbounded smoothness.
  arXiv  Detail & Related papers  (2024-01-17T20:28:15Z)
• Contextual Stochastic Bilevel Optimization [50.36775806399861]
  We introduce contextual bilevel optimization (CSBO) -- a bilevel optimization framework with the lower-level problem minimizing an expectation on some contextual information and the upper-level variable. It is important for applications such as meta-learning, personalized learning, end-to-end learning, and Wasserstein distributionally robustly optimization with side information (WDRO-SI)
  arXiv  Detail & Related papers  (2023-10-27T23:24:37Z)
• Non-Convex Bilevel Optimization with Time-Varying Objective Functions [57.299128109226025]
  We propose an online bilevel optimization where the functions can be time-varying and the agent continuously updates the decisions with online data. Compared to existing algorithms, SOBOW is computationally efficient and does not need to know previous functions. We show that SOBOW can achieve a sublinear bilevel local regret under mild conditions.
  arXiv  Detail & Related papers  (2023-08-07T06:27:57Z)
• Fast Adaptive Federated Bilevel Optimization [14.579475552088692]
  We propose a novel adaptive federated bilevel optimization algorithm (i.e.,AdaFBiO) to solve the distributed bilevel optimization problems. AdaFBiO uses the unified adaptive matrices to flexibly incorporate various adaptive learning rates to update variables in both UL and LL problems. We provide a convergence analysis framework for our AdaFBiO algorithm, and prove it needs the sample of complexity of $tildeO(epsilon-3)$ with communication complexity of $tildeO(epsilon-2)$ to obtain an $
  arXiv  Detail & Related papers  (2022-11-02T13:55:47Z)
• Enhanced Bilevel Optimization via Bregman Distance [104.96004056928474]
  We propose a bilevel optimization method based on Bregman Bregman functions. We also propose an accelerated version of SBiO-BreD method (ASBiO-BreD) by using the variance-reduced technique.
  arXiv  Detail & Related papers  (2021-07-26T16:18:43Z)
• 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)

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.