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: 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.

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


Input: Consider Input: We propose a "plan online and learn offline" framework for the setting where an agent, with an internal model, needs to continually act and learn in the world. Our work builds on the synergistic relationship between local model-based control, global value function learning, and exploration. We study how local trajectory optimization can cope with approximation errors  in the value function, and can stabilize and accelerate value function learning. Conversely, we also study how approximate value functions can help reduce the planning horizon and allow for better policies beyond local solutions. Finally, we also demonstrate how trajectory optimization can be used to perform temporally coordinated exploration in conjunction with estimating uncertainty in value function approximation. This exploration is critical for fast and stable learning of the value function. Combining these components enable solutions to complex control tasks, like humanoid locomotion and dexterous in-hand manipulation, in the equivalent of a few minutes of experience in the real world.

Output: We propose a framework that incorporates planning for efficient exploration and learning in complex environments.


Input: Consider Input: Loss functions play a crucial role in deep metric learning thus a variety of them have been proposed. Some supervise the learning process by pairwise or tripletwise similarity constraints while others take the advantage of structured similarity information among multiple data points. In this work, we approach deep metric learning from a novel perspective. We propose instance cross entropy (ICE) which measures the difference between an estimated instance-level matching distribution and its ground-truth one. ICE has three main appealing properties. Firstly, similar to categorical cross entropy (CCE), ICE has clear probabilistic interpretation and exploits structured semantic similarity information for learning supervision. Secondly, ICE is scalable to infinite training data as it learns on mini-batches iteratively and is independent of the training set size. Thirdly, motivated by our relative weight analysis, seamless sample reweighting is incorporated. It rescales samples’ gradients to control the differentiation degree over training examples instead of truncating them by sample mining. In addition to its simplicity and intuitiveness, extensive experiments on three real-world benchmarks demonstrate the superiority of ICE.


Output: We propose instance cross entropy (ICE) which measures the difference between an estimated instance-level matching distribution and its ground-truth one.