In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Input: Consider Input: We propose order learning to determine the order graph of classes, representing ranks or priorities, and classify an object instance into one of the classes. To this end, we design a pairwise comparator to categorize the relationship between two instances into one of three cases: one instance is 'greater than,' 'similar to,' or 'smaller than' the other. Then, by comparing an input instance with reference instances and maximizing the consistency among the comparison results, the class of the input can be estimated reliably. We apply order learning to develop a facial age estimator, which provides the state-of-the-art performance. Moreover, the performance is further improved when the order graph is divided into disjoint chains using gender and ethnic group information or even in an unsupervised manner.

Output: The notion of order learning is proposed and it is applied to regression problems in computer vision

Input: Consider Input: Stochastic Gradient Descent or SGD is the most popular optimization algorithm for large-scale problems. SGD estimates the gradient by uniform sampling with sample size one. There have been several other works that suggest faster epoch wise convergence by using weighted non-uniform sampling for better gradient estimates. Unfortunately, the per-iteration cost of maintaining this adaptive distribution for gradient estimation is more than calculating the full gradient. As a result, the false impression of faster convergence in iterations leads to slower convergence in time, which we call a chicken-and-egg loop. In this paper, we break this barrier by providing the first demonstration of a sampling scheme, which leads to superior gradient estimation, while keeping the sampling cost per iteration similar to that of the uniform sampling. Such an algorithm is possible due to the sampling view of Locality Sensitive Hashing (LSH), which came to light recently. As a consequence of superior and fast estimation, we reduce the running time of all existing gradient descent algorithms. We demonstrate the benefits of our proposal on both SGD and AdaGrad.

Output: We improve the running of all existing gradient descent algorithms.

Input: Consider Input: We show how discrete objects can be learnt in an unsupervised fashion from pixels, and how to perform reinforcement learning using this object representation.

More precisely, we construct a differentiable mapping from an image to a discrete tabular list of objects, where each object consists of a differentiable position, feature vector, and scalar presence value that allows the representation to be learnt using an attention mechanism.

Applying this mapping to Atari games, together with an interaction net-style architecture for calculating quantities from objects, we construct agents that can play Atari games using objects learnt in an unsupervised fashion. During training, many natural objects emerge, such as the ball and paddles in Pong, and the submarine and fish in Seaquest.

This gives the first reinforcement learning agent for Atari with an interpretable object representation, and opens the avenue for agents that can conduct object-based exploration and generalization.
Output: We show how discrete objects can be learnt in an unsupervised fashion from pixels, and how to perform reinforcement learning using this object representation.