A Stochastic Approach to Bi-Level Optimization for Hyperparameter Optimization and Meta Learning

• URL: http://arxiv.org/abs/2410.10417v1
• Date: Mon, 14 Oct 2024 12:10:06 GMT
• Title: A Stochastic Approach to Bi-Level Optimization for Hyperparameter Optimization and Meta Learning
• Authors: Minyoung Kim, Timothy M. Hospedales,
• Abstract summary: We tackle the general differentiable meta learning problem that is ubiquitous in modern deep learning. These problems are often formalized as Bi-Level optimizations (BLO) We introduce a novel perspective by turning a given BLO problem into a ii optimization, where the inner loss function becomes a smooth distribution, and the outer loss becomes an expected loss over the inner distribution.
• Score: 74.80956524812714
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We tackle the general differentiable meta learning problem that is ubiquitous in modern deep learning, including hyperparameter optimization, loss function learning, few-shot learning, invariance learning and more. These problems are often formalized as Bi-Level optimizations (BLO). We introduce a novel perspective by turning a given BLO problem into a stochastic optimization, where the inner loss function becomes a smooth probability distribution, and the outer loss becomes an expected loss over the inner distribution. To solve this stochastic optimization, we adopt Stochastic Gradient Langevin Dynamics (SGLD) MCMC to sample inner distribution, and propose a recurrent algorithm to compute the MC-estimated hypergradient. Our derivation is similar to forward-mode differentiation, but we introduce a new first-order approximation that makes it feasible for large models without needing to store huge Jacobian matrices. The main benefits are two-fold: i) Our stochastic formulation takes into account uncertainty, which makes the method robust to suboptimal inner optimization or non-unique multiple inner minima due to overparametrization; ii) Compared to existing methods that often exhibit unstable behavior and hyperparameter sensitivity in practice, our method leads to considerably more reliable solutions. We demonstrate that the new approach achieves promising results on diverse meta learning problems and easily scales to learning 87M hyperparameters in the case of Vision Transformers.

Related papers

• Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oracles [23.648702140754967]
  We consider optimization when one only has to access biased oracles and obtain objective with low biases. We show that biased gradient methods can reduce variance in the non-varied regime. We also show that conditional optimization methods significantly improve best-known complexities in the literature for conditional optimization and risk optimization.
  arXiv  Detail & Related papers  (2024-08-20T17:56:16Z)
• Scalable Bayesian Meta-Learning through Generalized Implicit Gradients [64.21628447579772]
  Implicit Bayesian meta-learning (iBaML) method broadens the scope of learnable priors, but also quantifies the associated uncertainty. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one.
  arXiv  Detail & Related papers  (2023-03-31T02:10:30Z)
• Multistage Stochastic Optimization via Kernels [3.7565501074323224]
  We develop a non-parametric, data-driven, tractable approach for solving multistage optimization problems. We show that the proposed method produces decision rules with near-optimal average performance.
  arXiv  Detail & Related papers  (2023-03-11T23:19:32Z)
• A framework for bilevel optimization that enables stochastic and global variance reduction algorithms [17.12280360174073]
  Bilevel optimization is a problem of minimizing a value function which involves the arg-minimum of another function. We introduce a novel framework, in which the solution of the inner problem, the solution of the linear system, and the main variable evolve at the same time. We demonstrate that SABA, an adaptation of the celebrated SAGA algorithm in our framework, has $O(frac1T)$ convergence rate, and that it achieves linear convergence under Polyak-Lojasciewicz assumption.
  arXiv  Detail & Related papers  (2022-01-31T18:17:25Z)
• Neural Stochastic Dual Dynamic Programming [99.80617899593526]
  We introduce a trainable neural model that learns to map problem instances to a piece-wise linear value function. $nu$-SDDP can significantly reduce problem solving cost without sacrificing solution quality.
  arXiv  Detail & Related papers  (2021-12-01T22:55:23Z)
• High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [51.31435087414348]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity bounds with dependence on confidence level. We propose novel stepsize rules for two methods with gradient clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)
• Meta-Learning with Neural Tangent Kernels [58.06951624702086]
  We propose the first meta-learning paradigm in the Reproducing Kernel Hilbert Space (RKHS) induced by the meta-model's Neural Tangent Kernel (NTK) Within this paradigm, we introduce two meta-learning algorithms, which no longer need a sub-optimal iterative inner-loop adaptation as in the MAML framework. We achieve this goal by 1) replacing the adaptation with a fast-adaptive regularizer in the RKHS; and 2) solving the adaptation analytically based on the NTK theory.
  arXiv  Detail & Related papers  (2021-02-07T20:53:23Z)
• Convergence Properties of Stochastic Hypergradients [38.64355126221992]
  We study approximation schemes for the hypergradient, which are important when the lower-level problem is empirical risk on a large dataset. We provide numerical experiments to support our theoretical analysis and to show the advantage of using hypergradients in practice.
  arXiv  Detail & Related papers  (2020-11-13T20:50:36Z)
• Global Optimization of Gaussian processes [52.77024349608834]
  We propose a reduced-space formulation with trained Gaussian processes trained on few data points. The approach also leads to significantly smaller and computationally cheaper sub solver for lower bounding. In total, we reduce time convergence by orders of orders of the proposed method.
  arXiv  Detail & Related papers  (2020-05-21T20:59:11Z)

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.