Continuous-Time Meta-Learning with Forward Mode Differentiation

• URL: http://arxiv.org/abs/2203.01443v1
• Date: Wed, 2 Mar 2022 22:35:58 GMT
• Title: Continuous-Time Meta-Learning with Forward Mode Differentiation
• Authors: Tristan Deleu, David Kanaa, Leo Feng, Giancarlo Kerg, Yoshua Bengio, Guillaume Lajoie, Pierre-Luc Bacon
• Abstract summary: We introduce Continuous Meta-Learning (COMLN), a meta-learning algorithm where adaptation follows the dynamics of a gradient vector field. Treating the learning process as an ODE offers the notable advantage that the length of the trajectory is now continuous. We show empirically its efficiency in terms of runtime and memory usage, and we illustrate its effectiveness on a range of few-shot image classification problems.
• Score: 65.26189016950343
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Drawing inspiration from gradient-based meta-learning methods with infinitely small gradient steps, we introduce Continuous-Time Meta-Learning (COMLN), a meta-learning algorithm where adaptation follows the dynamics of a gradient vector field. Specifically, representations of the inputs are meta-learned such that a task-specific linear classifier is obtained as a solution of an ordinary differential equation (ODE). Treating the learning process as an ODE offers the notable advantage that the length of the trajectory is now continuous, as opposed to a fixed and discrete number of gradient steps. As a consequence, we can optimize the amount of adaptation necessary to solve a new task using stochastic gradient descent, in addition to learning the initial conditions as is standard practice in gradient-based meta-learning. Importantly, in order to compute the exact meta-gradients required for the outer-loop updates, we devise an efficient algorithm based on forward mode differentiation, whose memory requirements do not scale with the length of the learning trajectory, thus allowing longer adaptation in constant memory. We provide analytical guarantees for the stability of COMLN, we show empirically its efficiency in terms of runtime and memory usage, and we illustrate its effectiveness on a range of few-shot image classification problems.

Related papers

• 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)
• An Effective Dynamic Gradient Calibration Method for Continual Learning [11.555822066922508]
  Continual learning (CL) is a fundamental topic in machine learning, where the goal is to train a model with continuously incoming data and tasks. Due to the memory limit, we cannot store all the historical data, and therefore confront the catastrophic forgetting'' problem. We develop an effective algorithm to calibrate the gradient in each updating step of the model.
  arXiv  Detail & Related papers  (2024-07-30T16:30:09Z)
• Model-Agnostic Zeroth-Order Policy Optimization for Meta-Learning of Ergodic Linear Quadratic Regulators [13.343937277604892]
  We study the problem of using meta-learning to deal with uncertainty and heterogeneity in ergodic linear quadratic regulators. We propose an algorithm that omits the estimation of policy Hessian, which applies to tasks of learning a set of heterogeneous but similar linear dynamic systems. We provide a convergence result for the exact gradient descent process by analyzing the boundedness and smoothness of the gradient for the meta-objective.
  arXiv  Detail & Related papers  (2024-05-27T17:26:36Z)
• 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)
• Efficient Meta-Learning for Continual Learning with Taylor Expansion Approximation [2.28438857884398]
  Continual learning aims to alleviate catastrophic forgetting when handling consecutive tasks under non-stationary distributions. We propose a novel efficient meta-learning algorithm for solving the online continual learning problem. Our method achieves better or on-par performance and much higher efficiency compared to the state-of-the-art approaches.
  arXiv  Detail & Related papers  (2022-10-03T04:57:05Z)
• One Step at a Time: Pros and Cons of Multi-Step Meta-Gradient Reinforcement Learning [61.662504399411695]
  We introduce a novel method mixing multiple inner steps that enjoys a more accurate and robust meta-gradient signal. When applied to the Snake game, the mixing meta-gradient algorithm can cut the variance by a factor of 3 while achieving similar or higher performance.
  arXiv  Detail & Related papers  (2021-10-30T08:36:52Z)
• Meta-Learning with Adjoint Methods [16.753336086160598]
  A Meta-Learning (MAML) is widely used to find a good initialization for a family of tasks. Despite its success, a critical challenge in MAML is to calculate the gradient w.r.t the initialization of a long training trajectory for the sampled tasks. We propose Adjoint MAML (A-MAML) to address this problem. We demonstrate the advantage of our approach in both synthetic and real-world meta-learning tasks.
  arXiv  Detail & Related papers  (2021-10-16T01:18:50Z)
• Large-Scale Meta-Learning with Continual Trajectory Shifting [76.29017270864308]
  We show that allowing the meta-learners to take a larger number of inner gradient steps better captures the structure of heterogeneous and large-scale tasks. In order to increase the frequency of meta-updates, we propose to estimate the required shift of the task-specific parameters. We show that the algorithm largely outperforms the previous first-order meta-learning methods in terms of both generalization performance and convergence.
  arXiv  Detail & Related papers  (2021-02-14T18:36:33Z)
• Regularizing Meta-Learning via Gradient Dropout [102.29924160341572]
  meta-learning models are prone to overfitting when there are no sufficient training tasks for the meta-learners to generalize. We introduce a simple yet effective method to alleviate the risk of overfitting for gradient-based meta-learning.
  arXiv  Detail & Related papers  (2020-04-13T10:47:02Z)

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.