Methods from convex optimization are widely used as building blocks for deep learning algorithms. However, the reasons for their empirical success are unclear, since modern convolutional networks (convnets), incorporating rectifier units and max-pooling, are neither smooth nor convex. Standard guarantees therefore do not apply. This paper provides the first convergence rates for gradient descent on rectifier convnets. The proof utilizes the particular structure of rectifier networks which consists in binary active inactive gates applied on top of an underlying linear network. The approach generalizes to max-pooling, dropout and maxout. In other words, to precisely the neural networks that perform best empirically. The key step is to introduce gated games, an extension of convex games with similar convergence properties that capture the gating function of rectifiers. The main result is that rectifier convnets converge to a critical point at a rate controlled by the gated-regret of the units in the network. Corollaries of the main result include: (i) a game-theoretic description of the representations learned by a neural network; (ii) a logarithmic-regret algorithm for training neural nets; and (iii) a formal setting for analyzing conditional computation in neural nets that can be applied to recently developed models of attention.
The idea of decomposing deep learning algorithms into cooperating modules dates back to at least the work of Bottou @cite_85 . A related line of work modeling biological neural networks from a game-theoretic perspective can be found in @cite_49 @cite_20 @cite_54 @cite_51 .
@cite_54 @cite_85 @cite_49 @cite_51 @cite_20
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With the rise of data driven deep neural networks as a realization of universal function approximators, most research on computer vision problems has moved away from hand crafted classical image processing algorithms. This paper shows that with a well designed algorithm, we are capable of outperforming neural network based methods on the task of depth completion. The proposed algorithm is simple and fast, runs on the CPU, and relies only on basic image processing operations to perform depth completion of sparse LIDAR depth data. We evaluate our algorithm on the challenging KITTI depth completion benchmark, and at the time of submission, our method ranks first on the KITTI test server among all published methods. Furthermore, our algorithm is data independent, requiring no training data to perform the task at hand. The code written in Python will be made publicly available at this https URL Sequential decision making problems, such as structured prediction, robotic control, and game playing, require a combination of planning policies and generalisation of those plans. In this paper, we present Expert Iteration (ExIt), a novel reinforcement learning algorithm which decomposes the problem into separate planning and generalisation tasks. Planning new policies is performed by tree search, while a deep neural network generalises those plans. Subsequently, tree search is improved by using the neural network policy to guide search, increasing the strength of new plans. In contrast, standard deep Reinforcement Learning algorithms rely on a neural network not only to generalise plans, but to discover them too. We show that ExIt outperforms REINFORCE for training a neural network to play the board game Hex, and our final tree search agent, trained tabula rasa, defeats MoHex1.0, the most recent Olympiad Champion player to be publicly released. In 2015, Google's Deepmind announced an advancement in creating an autonomous agent based on deep reinforcement learning (DRL) that could beat a professional player in a series of 49 Atari games. However, the current manifestation of DRL is still immature, and has significant drawbacks. One of DRL's imperfections is its lack of "exploration" during the training process, especially when working with high-dimensional problems. In this paper, we propose a mixed strategy approach that mimics behaviors of human when interacting with environment, and create a "thinking" agent that allows for more efficient exploration in the DRL training process. The simulation results based on the Breakout game show that our scheme achieves a higher probability of obtaining a maximum score than does the baseline DRL algorithm, i.e., the asynchronous advantage actor-critic method. The proposed scheme therefore can be applied effectively to solving a complicated task in a real-world application. The convolutional neural network (CNN), which is one of the deep learning models, has seen much success in a variety of computer vision tasks. However, designing CNN architectures still requires expert knowledge and a lot of trial and error. In this paper, we attempt to automatically construct CNN architectures for an image classification task based on Cartesian genetic programming (CGP). In our method, we adopt highly functional modules, such as convolutional blocks and tensor concatenation, as the node functions in CGP. The CNN structure and connectivity represented by the CGP encoding method are optimized to maximize the validation accuracy. To evaluate the proposed method, we constructed a CNN architecture for the image classification task with the CIFAR-10 dataset. The experimental result shows that the proposed method can be used to automatically find the competitive CNN architecture compared with state-of-the-art models.