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Register a new userMeta-Learning with Differentiable Convex Optimization
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Added by
Kwonjoon Lee
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Many meta-learning approaches for few-shot learning rely on simple base learners such as nearest-neighbor classifiers. However, even in the few-shot regime, discriminatively trained linear predictors can offer better generalization. We propose to use these predictors as base learners to learn representations for few-shot learning and show they offer better tradeoffs between feature size and performance across a range of few-shot recognition benchmarks. Our objective is to learn feature embeddings that generalize well under a linear classification rule for novel categories. To efficiently solve the objective, we exploit two properties of linear classifiers: implicit differentiation of the optimality conditions of the convex problem and the dual formulation of the optimization problem. This allows us to use high-dimensional embeddings with improved generalization at a modest increase in computational overhead. Our approach, named MetaOptNet, achieves state-of-the-art performance on miniImageNet, tieredImageNet, CIFAR-FS, and FC100 few-shot learning benchmarks. Our code is available at https://github.com/kjunelee/MetaOptNet.
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Adapting deep networks to new concepts from a few examples is challenging, due to the high computational requirements of standard fine-tuning procedures. Most work on few-shot learning has thus focused on simple learning techniques for adaptation, such as nearest neighbours or gradient descent. Nonetheless, the machine learning literature contains a wealth of methods that learn non-deep models very efficiently. In this paper, we propose to use these fast convergent methods as the main adaptation mechanism for few-shot learning. The main idea is to teach a deep network to use standard machine learning tools, such as ridge regression, as part of its own internal model, enabling it to quickly adapt to novel data. This requires back-propagating errors through the solver steps. While normally the cost of the matrix operations involved in such a process would be significant, by using the Woodbury identity we can make the small number of examples work to our advantage. We propose both closed-form and iterative solvers, based on ridge regression and logistic regression components. Our methods constitute a simple and novel approach to the problem of few-shot learning and achieve performance competitive with or superior to the state of the art on three benchmarks.
Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach to differentiating through disciplined convex programs, a subclass of convex optimization problems used by domain-specific languages (DSLs) for convex optimization. We introduce disciplined parametrized programming, a subset of disciplined convex programming, and we show that every disciplined parametrized program can be represented as the composition of an affine map from parameters to problem data, a solver, and an affine map from the solvers solution to a solution of the original problem (a new form we refer to as affine-solver-affine form). We then demonstrate how to efficiently differentiate through each of these components, allowing for end-to-end analytical differentiation through the entire convex program. We implement our methodology in version 1.1 of CVXPY, a popular Python-embedded DSL for convex optimization, and additionally implement differentiable layers for disciplined convex programs in PyTorch and TensorFlow 2.0. Our implementation significantly lowers the barrier to using convex optimization problems in differentiable programs. We present applications in linear machine learning models and in stochastic control, and we show that our layer is competitive (in execution time) compared to specialized differentiable solvers from past work.
The ability to walk in new scenarios is a key milestone on the path toward real-world applications of legged robots. In this work, we introduce Meta Strategy Optimization, a meta-learning algorithm for training policies with latent variable inputs that can quickly adapt to new scenarios with a handful of trials in the target environment. The key idea behind MSO is to expose the same adaptation process, Strategy Optimization (SO), to both the training and testing phases. This allows MSO to effectively learn locomotion skills as well as a latent space that is suitable for fast adaptation. We evaluate our method on a real quadruped robot and demonstrate successful adaptation in various scenarios, including sim-to-real transfer, walking with a weakened motor, or climbing up a slope. Furthermore, we quantitatively analyze the generalization capability of the trained policy in simulated environments. Both real and simulated experiments show that our method outperforms previous methods in adaptation to novel tasks.
To address the annotation scarcity issue in some cases of semantic segmentation, there have been a few attempts to develop the segmentation model in the few-shot learning paradigm. However, most existing methods only focus on the traditional 1-way segmentation setting (i.e., one image only contains a single object). This is far away from practical semantic segmentation tasks where the K-way setting (K>1) is usually required by performing the accurate multi-object segmentation. To deal with this issue, we formulate the few-shot semantic segmentation task as a learning-based pixel classification problem and propose a novel framework called MetaSegNet based on meta-learning. In MetaSegNet, an architecture of embedding module consisting of the global and local feature branches is developed to extract the appropriate meta-knowledge for the few-shot segmentation. Moreover, we incorporate a linear model into MetaSegNet as a base learner to directly predict the label of each pixel for the multi-object segmentation. Furthermore, our MetaSegNet can be trained by the episodic training mechanism in an end-to-end manner from scratch. Experiments on two popular semantic segmentation datasets, i.e., PASCAL VOC and COCO, reveal the effectiveness of the proposed MetaSegNet in the K-way few-shot semantic segmentation task.
Many control policies used in various applications determine the input or action by solving a convex optimization problem that depends on the current state and some parameters. Common examples of such convex optimization control policies (COCPs) include the linear quadratic regulator (LQR), convex model predictive control (MPC), and convex control-Lyapunov or approximate dynamic programming (ADP) policies. These types of control policies are tuned by varying the parameters in the optimization problem, such as the LQR weights, to obtain good performance, judged by application-specific metrics. Tuning is often done by hand, or by simple methods such as a crude grid search. In this paper we propose a method to automate this process, by adjusting the parameters using an approximate gradient of the performance metric with respect to the parameters. Our method relies on recently developed methods that can efficiently evaluate the derivative of the solution of a convex optimization problem with respect to its parameters. We illustrate our method on several examples.
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