Meta-Learning through Coupled Optimization in Reproducing Kernel Hilbert Spaces

Juan, Cervino,; Bazerque, Juan Andrés; Calvo-Fullana, Miguel; Ribeiro, Alejandro

doi:10.23919/acc.2019.8814419

Cited by 5 publications

(5 citation statements)

References 6 publications

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“…, N for cross-learning, with the architecture being based on AlexNet [17] with a reduction on the size of the last fully connected layers to 256 neurons per layer, corresponding to θ ∈ R S , with S = 4,911,745. In this case, it is crucial to make use of the cross-learning projection (10) in the dual domain, thus reducing the dimensionality from S to N = 4 variables. Further, we split the dataset in two parts, using 4/5 of the images for training and 1/5 for testing.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…By combining the gradient step given in equation ( 9) with the projection (10), we obtain the cross-learning algorithm illustrated in Algorithm 1. This takes the form to a projected gradient descent, which can be shown to converge to the optimal value of the cross-learning problem (PCL) in the case of a convex problems [13].…”

Section: Algorithm Constructionmentioning

confidence: 99%

“…On a neural network the function parameterization vectors θi may have millions of parameters rendering projection (10) challenging in practice. However, we can exploit the fact that only one constraint is added per function, resorting to a dual domain algorithm which has Algorithm 2 Cross-learning projection 1: Initialize µi = µ 0 i and prescribe error δ > 0 2: repeat for k = 0, 1, .…”

Section: Projection In the Dual Domainmentioning

confidence: 99%

“…In this paper, we take a constrained approach to the multi-task learning problem. Our formulation is based on the cross-learning framework [10,11]. Originally used for learning policies in a reinforcement learning scenario, nevertheless, its principles can be also applied to the multi-task supervised learning problem.…”

Section: Introductionmentioning

confidence: 99%

“…As µ must be nonnegative [15], we project them to the nonnegative orthant at every step. The stopping condition of Algorithm 2 is the duality gap of the projection (10), which can be made arbitrarily small. Note that the cross-learning projection ( 10) is a convex problem, thus once the algorithm is halted, the optimal parameters {θi}, θg of the problem are recovered by using the primal solution ( 12) and (13).…”

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confidence: 99%

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Multi-task Supervised Learning via Cross-learning

Juan¹,

Bazerque²,

Calvo-Fullana³

et al. 2020

Preprint

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In this paper we consider a problem known as multi-task learning, consisting of fitting a set of classifier or regression functions intended for solving different tasks. In our novel formulation, we couple the parameters of these functions, so that they learn in their task specific domains while staying close to each other. This facilitates cross-fertilization in which data collected across different domains help improving the learning performance at each other task. First, we present a simplified case in which the goal is to estimate the means of two Gaussian variables, for the purpose of gaining some insights on the advantage of the proposed cross-learning strategy. Then we provide a stochastic projected gradient algorithm to perform crosslearning over a generic loss function. If the number of parameters is large, then the projection step becomes computationally expensive. To avoid this situation, we derive a primal-dual algorithm that exploits the structure of the dual problem, achieving a formulation whose complexity only depends on the number of tasks. Preliminary numerical experiments for image classification by neural networks trained on a dataset divided in different domains corroborate that the cross-learned function outperforms both the task-specific and the consensus approaches.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Algorithm Constructionmentioning

confidence: 99%

Section: Projection In the Dual Domainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Multi-task Supervised Learning via Cross-learning

Juan¹,

Bazerque²,

Calvo-Fullana³

et al. 2020

Preprint

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Multi-Task Bias-Variance Trade-Off Through Functional Constraints

Juan

Bazerque

Calvo-Fullana

et al. 2023

ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Sufficiently Accurate Model Learning

Zhang

Khan

Paternain

et al. 2020

2020 IEEE International Conference on Robotics and Automation (ICRA)

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Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions. This can be improved using prior knowledge about the task at hand, which can be encoded in the form of constraints. This turns the unconstrained model learning problem into a constrained one. These constraints allow models with finite capacity to focus their expressive power on important aspects of the system. This can lead to models that are better suited for certain tasks. This paper introduces the constrained Sufficiently Accurate model learning approach, provides examples of such problems, and presents a theorem on how close some approximate solutions can be. The approximate solution quality will depend on the function parameterization, loss and constraint function smoothness, and the number of samples in model learning.

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Meta-Learning through Coupled Optimization in Reproducing Kernel Hilbert Spaces

Cited by 5 publications

References 6 publications

Multi-task Supervised Learning via Cross-learning

Multi-task Supervised Learning via Cross-learning

Multi-Task Bias-Variance Trade-Off Through Functional Constraints

Sufficiently Accurate Model Learning

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