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: Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Rate-optimal procedures such as Tukey's median and other estimators based on statistical depth functions are impractical because of their computational intractability. In this paper, we establish an intriguing connection between f-GANs and various depth functions through the lens of f-Learning. Similar to the derivation of f-GAN, we show that these depth functions that lead to rate-optimal robust estimators can all be viewed as variational lower bounds of the total variation distance in the framework of f-Learning. This connection opens the door of computing robust estimators using tools developed for training GANs. In particular, we show that a JS-GAN that uses a neural network discriminator with at least one hidden layer is able to achieve the minimax rate of robust mean estimation under Huber's $\epsilon$-contamination model. Interestingly, the hidden layers of the neural net structure in the discriminator class are shown to be necessary for robust estimation.

Answer: GANs are shown to provide us a new effective robust mean estimate against agnostic contaminations with both statistical optimality and practical tractability.


Question: We consider reinforcement learning and bandit structured prediction problems with very sparse loss feedback: only at the end of an episode. We introduce a novel algorithm, RESIDUAL LOSS PREDICTION (RESLOPE), that solves such problems by automatically learning an internal representation of a denser reward function. RESLOPE operates as a reduction to contextual bandits, using its learned loss representation to solve the credit assignment problem, and a contextual bandit oracle to trade-off exploration and exploitation. RESLOPE enjoys a no-regret reduction-style theoretical guarantee and outperforms state of the art reinforcement learning algorithms in both MDP environments and bandit structured prediction settings.

Answer: We present a novel algorithm for solving reinforcement learning and bandit structured prediction problems with very sparse loss feedback.


Question: Despite its empirical success, the theoretical underpinnings of the stability, convergence and acceleration properties of batch normalization (BN) remain elusive. In this paper, we attack this problem from a modelling approach, where we perform thorough theoretical analysis on BN applied to simplified model: ordinary least squares (OLS). We discover that gradient descent on OLS with BN has interesting properties, including a scaling law, convergence for arbitrary learning rates for the weights, asymptotic acceleration effects, as well as insensitivity to choice of learning rates. We then demonstrate numerically that these findings are not specific to the OLS problem and hold qualitatively for more complex supervised learning problems. This points to a new direction towards uncovering the mathematical principles that underlies batch normalization.

Answer:
We mathematically analyze the effect of batch normalization on a simple model and obtain key new insights that applies to general supervised learning.