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: We compare the model-free reinforcement learning with the model-based approaches through the lens of the expressive power of neural networks for policies, $Q$-functions, and dynamics.   We show, theoretically and empirically, that even for one-dimensional continuous state space, there are many MDPs whose optimal $Q$-functions and policies are much more complex than the dynamics. We hypothesize many real-world MDPs also have a similar property. For these MDPs, model-based planning is a favorable algorithm, because the resulting policies can approximate the optimal policy significantly better than a neural network parameterization can, and model-free or model-based policy optimization rely on policy parameterization. Motivated by the theory, we apply a simple multi-step model-based bootstrapping planner (BOOTS) to bootstrap a weak $Q$-function into a stronger policy. Empirical results show that applying BOOTS on top of model-based or model-free policy optimization algorithms at the test time improves the performance on MuJoCo benchmark tasks.

Answer: We compare deep model-based and model-free RL algorithms by studying the approximability of $Q$-functions, policies, and dynamics by neural networks. 


Question: Sequence prediction models can be learned from example sequences with a variety of training algorithms. Maximum likelihood learning is simple and efficient, yet can suffer from compounding error at test time. 
 Reinforcement learning such as policy gradient addresses the issue but can have prohibitively poor exploration efficiency. A rich set of other algorithms, such as data noising, RAML, and softmax policy gradient, have also been developed from different perspectives. 
 In this paper, we present a formalism of entropy regularized policy optimization, and show that the apparently distinct algorithms, including MLE, can be reformulated as special instances of the formulation. The difference between them is characterized by the reward function and two weight hyperparameters.
 The unifying interpretation enables us to systematically compare the algorithms side-by-side, and gain new insights into the trade-offs of the algorithm design.
 The new perspective also leads to an improved approach that dynamically interpolates among the family of algorithms, and learns the model in a scheduled way. Experiments on machine translation, text summarization, and game imitation learning demonstrate superiority of the proposed approach.

Answer:
An entropy regularized policy optimization formalism subsumes a set of sequence prediction learning algorithms. A new interpolation algorithm with improved results on text generation and game imitation learning.