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.

[Q]: In recent years several adversarial attacks and defenses have been proposed. Often seemingly robust models turn out to be non-robust when more sophisticated attacks are used. One way out of this dilemma are provable robustness guarantees. While provably robust models for specific $l_p$-perturbation models have been developed, we show that they do not come with any guarantee against other $l_q$-perturbations. We propose a new regularization scheme, MMR-Universal, for ReLU networks which enforces robustness wrt $l_1$- extit{and} $l_\infty$-perturbations and show how that leads to the first provably robust models wrt any $l_p$-norm for $p\geq 1$.
[A]: We introduce a method to train models with provable robustness wrt all the $l_p$-norms for $p\geq 1$ simultaneously.

[Q]: Deep reinforcement learning (DRL) algorithms have demonstrated progress in learning to find a goal in challenging environments. As the title of the paper by Mirowski et al. (2016) suggests, one might assume that DRL-based algorithms are able to "learn to navigate" and are thus ready to replace classical mapping and path-planning algorithms, at least in simulated environments. Yet, from experiments and analysis in this earlier work, it is not clear what strategies are used by these algorithms in navigating the mazes and finding the goal. In this paper, we pose and study this underlying question: are DRL algorithms doing some form of mapping and/or path-planning? Our experiments show that the algorithms are not memorizing the maps of mazes at the testing stage but, rather, at the training stage. Hence, the DRL algorithms fall short of qualifying as mapping or path-planning algorithms with any reasonable definition of mapping. We extend the experiments in Mirowski et al. (2016) by separating the set of training and testing maps and by a more ablative coverage of the space of experiments. Our systematic experiments show that the NavA3C-D1-D2-L algorithm, when trained and tested on the same maps, is able to choose the shorter paths to the goal. However, when tested on unseen maps the algorithm utilizes a wall-following strategy to find the goal without doing any mapping or path planning.
[A]: We quantitatively and qualitatively evaluate deep reinforcement learning based navigation methods under a variety of conditions to answer the question of how close they are to replacing classical path planners and mapping algorithms.

[Q]: The information bottleneck (IB) problem tackles the issue of obtaining relevant compressed representations T of some random variable X for the task of predicting Y. It is defined as a constrained optimization problem which maximizes the information the representation has about the task, I(T;Y), while ensuring that a minimum level of compression r is achieved (i.e., I(X;T) <= r). For practical reasons the problem is usually solved by maximizing the IB Lagrangian for many values of the Lagrange multiplier, therefore drawing the IB curve (i.e., the curve of maximal I(T;Y) for a given I(X;Y)) and selecting the representation of desired predictability and compression. It is known when Y is a deterministic function of X, the IB curve cannot be explored and other Lagrangians have been proposed to tackle this problem (e.g., the squared IB Lagrangian). In this paper we (i) present a general family of Lagrangians which allow for the exploration of the IB curve in all scenarios; (ii) prove that if these Lagrangians are used, there is a one-to-one mapping between the Lagrange multiplier and the desired compression rate r for known IB curve shapes, hence, freeing from the burden of solving the optimization problem for many values of the Lagrange multiplier.
[A]:
We introduce a general family of Lagrangians that allow exploring the IB curve in all scenarios. When these are used, and the IB curve is known, one can optimize directly for a performance/compression level directly.