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.
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Question: Optimization algorithms for training deep models not only affects the convergence rate and stability of the training process, but are also highly related to the generalization performance of trained models. While adaptive algorithms, such as Adam and RMSprop, have shown better optimization performance than stochastic gradient descent (SGD) in many scenarios, they often lead to worse generalization performance than SGD, when used for training deep neural networks (DNNs). In this work, we identify two problems regarding the direction and step size for updating the weight vectors of hidden units, which may degrade the generalization performance of Adam. As a solution, we propose the normalized direction-preserving Adam (ND-Adam) algorithm, which controls the update direction and step size more precisely, and thus bridges the generalization gap between Adam and SGD. Following a similar rationale, we further improve the generalization performance in classification tasks by regularizing the softmax logits. By bridging the gap between SGD and Adam, we also shed some light on why certain optimization algorithms generalize better than others.

Answer: A tailored version of Adam for training DNNs, which bridges the generalization gap between Adam and SGD.


Question: 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.

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


Question: We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable model founded on game theory for understanding the aggregate effect of individual actions and predicting the temporal evolution of population distributions. We achieve a synthesis of MFG and Markov decision processes (MDP) by showing that a special MFG is reducible to an MDP. This enables us to broaden the scope of mean field game theory and infer MFG models of large real-world systems via deep inverse reinforcement learning. Our method learns both the reward function and forward dynamics of an MFG from real data, and we report the first empirical test of a mean field game model of a real-world social media population.

Answer:
Inference of a mean field game (MFG) model of large population behavior via a synthesis of MFG and Markov decision processes.