Meta-Learning with Warped Gradient Descent
Learning an efficient update rule from data that promotes rapid learning of new tasks from the same distribution remains an open problem in meta-learning. Typically, previous works have approached this issue either by attempting to train a neural network that directly produces updates or by attempting to learn better initialisations or scaling factors for a gradient-based update rule. Both these approaches pose challenges. On one hand, directly producing an update forgoes a useful inductive bias and can easily lead to non-converging behaviour. On the other hand, approaches that try to control a gradient-based update rule typically resort to computing gradients through the learning process to obtain their meta-gradients, leading to methods that can not scale beyond few-shot task adaptation. In this work we propose Warped Gradient Descent (WarpGrad), a method that intersects these approaches to mitigate their limitations. WarpGrad meta-learns an efficiently parameterised preconditioning matrix that facilitates gradient descent across the task distribution. Preconditioning arises by interleaving non-linear layers, referred to as warp-layers, between the layers of a task-learner. Warp-layers are meta-learned without backpropagating through the task training process in a manner similar to methods that learn to directly produce updates. WarpGrad is computationally efficient, easy to implement, and can scale to arbitrarily large meta-learning problems. We provide a geometrical interpretation of the approach and evaluate its effectiveness in a variety of settings, including few-shot, standard supervised, continual and reinforcement learning.
The authors propose warped gradient descent (WarpGrad) an optimisation framework for facilitating gradient-based meta-learning. WarpGrad interleaves within the learner meta-learned warp-layers that implicitly precondition the gradients of the task-specific parameters during backpropagation. In contrast to the linear projection layers employed in T-Nets, warp-layers are unrestricted in form and induce a full Jacobian preconditioning matrix. The warp layers are meta-learned in a trajectory-agnostic fashion, thus obviating the need to backpropagate through the gradient steps to compute the updates of their parameters. The framework is readily applicable to standard gradient-based meta-learners, and is shown to yield a significant boost in performance on both few-shot and multi-shot learning tasks, as well as to have promising applications to continual learning. The paper is well-structured and well-motivated: the problem statement is clearly laid out from the outset, with appropriate context, and explanations supported well diagramatically. The idea, and perhaps more so the applications thereof, is seemingly novel and its explanation is given straightforwardly while avoiding getting bogged down in technical details. Clear comparisons and distinctions with previous work are drawn - for instance with the update rules for several gradient-based methods - MAML and its derivatives - being laid out in standard form (though it might also be nice to echo this with the WarpGrad update rule). The experiments are logically ordered with the initial set covering the standard few-shot learning benchmarks with appropriate baselines (though the results for few-shot tieredImageNet are lacking in this respect), with most essential details given in the main text and full details, including those related to the datasets in question and hyperparameter selection, documented in Appendix H. Meta-learning does seem uniquely well-positioned for tackling the task of continual learning and it*s heartening to see this being explored here with a degree of success - it would be interested to see how its performance compares with standard continual learning methods (such as EWC) on the same task. Particularly impressive is the depth into which the Appendices regarding the experiments, both elaborating on the details given in the main text as well as additional ablation studies. Minor errors: - Page 7: *a neural network that dynamically **adapt** the parameters...* - should be *adapts* - Page 22: *where is the **identify** matrix* - should be *identity* - Page 27: *The task target function is **partition** into 5 sets of **sub-task*** - should be *partitioned* and *sub-tasks*, respectively
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### Title + Abstract
Meta-Learning with Warped Gradient Descent
Learning an efficient update rule from data that promotes rapid learning of new tasks from the same distribution remains an open problem in meta-learning. Typically, previous works have approached this issue either by attempting to train a neural network that directly produces updates or by attempting to learn better initialisations or scaling factors for a gradient-based update rule. Both these approaches pose challenges. On one hand, directly producing an update forgoes a useful inductive bias and can easily lead to non-converging behaviour. On the other hand, approaches that try to control a gradient-based update rule typically resort to computing gradients through the learning process to obtain their meta-gradients, leading to methods that can not scale beyond few-shot task adaptation. In this work we propose Warped Gradient Descent (WarpGrad), a method that intersects these approaches to mitigate their limitations. WarpGrad meta-learns an efficiently parameterised preconditioning matrix that facilitates gradient descent across the task distribution. Preconditioning arises by interleaving non-linear layers, referred to as warp-layers, between the layers of a task-learner. Warp-layers are meta-learned without backpropagating through the task training process in a manner similar to methods that learn to directly produce updates. WarpGrad is computationally efficient, easy to implement, and can scale to arbitrarily large meta-learning problems. We provide a geometrical interpretation of the approach and evaluate its effectiveness in a variety of settings, including few-shot, standard supervised, continual and reinforcement learning.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



The authors propose warped gradient descent (WarpGrad) an optimisation framework for facilitating gradient-based meta-learning. WarpGrad interleaves within the learner meta-learned warp-layers that implicitly precondition the gradients of the task-specific parameters during backpropagation. In contrast to the linear projection layers employed in T-Nets, warp-layers are unrestricted in form and induce a full Jacobian preconditioning matrix. The warp layers are meta-learned in a trajectory-agnostic fashion, thus obviating the need to backpropagate through the gradient steps to compute the updates of their parameters. The framework is readily applicable to standard gradient-based meta-learners, and is shown to yield a significant boost in performance on both few-shot and multi-shot learning tasks, as well as to have promising applications to continual learning. The paper is well-structured and well-motivated: the problem statement is clearly laid out from the outset, with appropriate context, and explanations supported well diagramatically. The idea, and perhaps more so the applications thereof, is seemingly novel and its explanation is given straightforwardly while avoiding getting bogged down in technical details. Clear comparisons and distinctions with previous work are drawn - for instance with the update rules for several gradient-based methods - MAML and its derivatives - being laid out in standard form (though it might also be nice to echo this with the WarpGrad update rule). The experiments are logically ordered with the initial set covering the standard few-shot learning benchmarks with appropriate baselines (though the results for few-shot tieredImageNet are lacking in this respect), with most essential details given in the main text and full details, including those related to the datasets in question and hyperparameter selection, documented in Appendix H. Meta-learning does seem uniquely well-positioned for tackling the task of continual learning and it*s heartening to see this being explored here with a degree of success - it would be interested to see how its performance compares with standard continual learning methods (such as EWC) on the same task. Particularly impressive is the depth into which the Appendices regarding the experiments, both elaborating on the details given in the main text as well as additional ablation studies. Minor errors: - Page 7: *a neural network that dynamically **adapt** the parameters...* - should be *adapts* - Page 22: *where is the **identify** matrix* - should be *identity* - Page 27: *The task target function is **partition** into 5 sets of **sub-task*** - should be *partitioned* and *sub-tasks*, respectively
assistant
The authors propose warped gradient descent (WarpGrad) an optimisation framework for facilitating gradient-based meta-learning. WarpGrad interleaves within the learner meta-learned warp-layers that implicitly precondition the gradients of the task-specific parameters during backpropagation. In contrast to the linear projection layers employed in T-Nets, warp-layers are unrestricted in form and induce a full Jacobian preconditioning matrix. The warp layers are meta-learned in a trajectory-agnostic fashion, thus obviating the need to backpropagate through the gradient steps to compute the updates of their parameters. The framework is readily applicable to standard gradient-based meta-learners, and is shown to yield a significant boost in performance on both few-shot and multi-shot learning tasks, as well as to have promising applications to continual learning. The paper is well-structured and well-motivated: the problem statement is clearly laid out from the outset, with appropriate context, and explanations supported well diagramatically. The idea, and perhaps more so the applications thereof, is seemingly novel and its explanation is given straightforwardly while avoiding getting bogged down in technical details. Clear comparisons and distinctions with previous work are drawn - for instance with the update rules for several gradient-based methods - MAML and its derivatives - being laid out in standard form (though it might also be nice to echo this with the WarpGrad update rule). The experiments are logically ordered with the initial set covering the standard few-shot learning benchmarks with appropriate baselines (though the results for few-shot tieredImageNet are lacking in this respect), with most essential details given in the main text and full details, including those related to the datasets in question and hyperparameter selection, documented in Appendix H. Meta-learning does seem uniquely well-positioned for tackling the task of continual learning and it*s heartening to see this being explored here with a degree of success - it would be interested to see how its performance compares with standard continual learning methods (such as EWC) on the same task. Particularly impressive is the depth into which the Appendices regarding the experiments, both elaborating on the details given in the main text as well as additional ablation studies. Minor errors: - Page 7: *a neural network that dynamically **adapt** the parameters...* - should be *adapts* - Page 22: *where is the **identify** matrix* - should be *identity* - Page 27: *The task target function is **partition** into 5 sets of **sub-task*** - should be *partitioned* and *sub-tasks*, respectively