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1. Scalable Bayesian Meta-Learning through Generalized Implicit Gradients

   https://doi.org/10.1609/aaai.v37i9.26337  

   Zhang, Yilang; Li, Bingcong; Gao, Shijian; Giannakis, Georgios B. (June 2023, Proceedings of the AAAI Conference on Artificial Intelligence)

   Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces scalability issues when the inner-level optimization relies on gradient-based iterations. Implicit differentiation has been considered to alleviate this challenge, but it is restricted to an isotropic Gaussian prior, and only favors deterministic meta-learning approaches. This work markedly mitigates the scalability bottleneck by cross-fertilizing the benefits of implicit differentiation to probabilistic Bayesian meta-learning. The novel implicit Bayesian meta-learning (iBaML) method not only broadens the scope of learnable priors, but also quantifies the associated uncertainty. Furthermore, the ultimate complexity is well controlled regardless of the inner-level optimization trajectory. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one. Extensive numerical tests are also carried out to empirically validate the performance of the proposed method. 

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2. Meta-Learning with Implicit Gradients

   Rajeswaran, Aravind; Finn, Chelsea; Kakade, Sham; Levine, Sergey (January 2019, Advances in neural information processing systems)

   A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific models are learned in the inner-loop, by using only a small amount of data from the current task. A key challenge in scaling these approaches is the need to differentiate through the inner loop learning process, which can impose considerable computational and memory burdens. By drawing upon implicit differentiation, we develop the implicit MAML algorithm, which depends only on the solution to the inner level optimization and not the path taken by the inner loop optimizer. This effectively decouples the meta-gradient computation from the choice of inner loop optimizer. As a result, our approach is agnostic to the choice of inner loop optimizer and can gracefully handle many gradient steps without vanishing gradients or memory constraints. Theoretically, we prove that implicit MAML can compute accurate meta-gradients with a memory footprint that is, up to small constant factors, no more than that which is required to compute a single inner loop gradient and at no overall increase in the total computational cost. Experimentally, we show that these benefits of implicit MAML translate into empirical gains on few-shot image recognition benchmarks. 

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3. BOME! Bilevel Optimization Made Easy: A Simple First-Order Approach

   Bo Liu; Mao Ye; Stephen Wright; Peter Stone; Qiang Liu (January 2022, Advances in neural information processing systems)

   Bilevel optimization (BO) is useful for solving a variety of important machine learning problems including but not limited to hyperparameter optimization, meta- learning, continual learning, and reinforcement learning. Conventional BO methods need to differentiate through the low-level optimization process with implicit dif- ferentiation, which requires expensive calculations related to the Hessian matrix. There has been a recent quest for first-order methods for BO, but the methods pro- posed to date tend to be complicated and impractical for large-scale deep learning applications. In this work, we propose a simple first-order BO algorithm that de- pends only on first-order gradient information, requires no implicit differentiation, and is practical and efficient for large-scale non-convex functions in deep learning. We provide a non-asymptotic convergence analysis of the proposed method to stationary points for non-convex objectives and present empirical results that show its superior practical performance. 

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4. Communication-efficient federated hypergradient computation via aggregated iterative differentiation

   Xiao, P; Ji, K (July 2023, International Conference on Machine Learning)

   Federated bilevel optimization has attracted increasing attention due to emerging machine learning and communication applications. The biggest challenge lies in computing the gradient of the upper-level objective function (ie, hypergradient) in the federated setting due to the nonlinear and distributed construction of a series of global Hessian matrices. In this paper, we propose a novel communication-efficient federated hypergradient estimator via aggregated iterative differentiation (AggITD). AggITD is simple to implement and significantly reduces the communication cost by conducting the federated hypergradient estimation and the lower-level optimization simultaneously. We show that the proposed AggITD-based algorithm achieves the same sample complexity as existing approximate implicit differentiation (AID)-based approaches with much fewer communication rounds in the presence of data heterogeneity. Our results also shed light on the great advantage of ITD over AID in the federated/distributed hypergradient estimation. This differs from the comparison in the non-distributed bilevel optimization, where ITD is less efficient than AID. Our extensive experiments demonstrate the great effectiveness and communication efficiency of the proposed method. 

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5. Few Is Enough: Task-Augmented Active Meta-learning for Brain Cell Classification

   https://doi.org/10.1007/978-3-030-59710-8_36  

   Yuan, Pengyu; Mobiny, Aryan; Jahanipour, Jahandar; Li, Xiaoyang; Cicalese, Pietro; Roysam, Badrinath; Patel, Vishal; Dragan, Maric; Nguyen, Hien V. (January 2020, Medical Image Computing and Computer Assisted Intervention)

   null (Ed.)

   Deep Neural Networks (or DNNs) must constantly cope with distribution changes in the input data when the task of interest or the data collection protocol changes. Retraining a network from scratch to combat this issue poses a significant cost. Meta-learning aims to deliver an adaptive model that is sensitive to these underlying distribution changes, but requires many tasks during the meta-training process. In this paper, we propose a tAsk-auGmented actIve meta-LEarning (AGILE) method to efficiently adapt DNNs to new tasks by using a small number of training examples. AGILE combines a meta-learning algorithm with a novel task augmentation technique which we use to generate an initial adaptive model. It then uses Bayesian dropout uncertainty estimates to actively select the most difficult samples when updating the model to a new task. This allows AGILE to learn with fewer tasks and a few informative samples, achieving high performance with a limited dataset. We perform our experiments using the brain cell classification task and compare the results to a plain meta-learning model trained from scratch. We show that the proposed task-augmented meta-learning framework can learn to classify new cell types after a single gradient step with a limited number of training samples. We show that active learning with Bayesian uncertainty can further improve the performance when the number of training samples is extremely small. Using only 1% of the training data and a single update step, we achieved 90% accuracy on the new cell type classification task, a 50% points improvement over a state-of-the-art meta-learning algorithm. 

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