Overview and Summary This paper presents a method for motion planning where the cost of evaluating transitions between robot configurations is high. The problem is formulated as a graph-search algorithm, where the order of graph expansion has a large impact on the performance of the algorithm due to the edge expansion cost. The paper uses ideas from optimal test selection in order to derive the resulting algorithm. The algorithm is tested on a number of synthetic datasets, a simulator, and a real-world helicopter planning problem. Detailed Comments This paper extended work within the well-studied domain of robotic motion planning, extending and combining prior work in the area to construct a new algorithm.

The authors propose a reinforcement learning strategy to learn new heuristic (specifically, greedy) strategies for solving graph-based combinatorial problems. An RL framework is combined with a graph embedding approach. The RL approach effectively learns a greedy policy for selecting constructing an approximate solution. The approach is innovative and the empirical results appear promising. An important advantage of the work is that the learned policy is not restricted to a fixed problem size, in contrast to earlier work.

SUMMARY: The paper proposes an algorithm that combines imitation learning with tree search, which results in an apprentice learning from an ever-improving expert. A DQN is trained to learn a policy derived from an MCTS agent, with the DQN providing generalisation to unseen states. It is also then used as feedback to improve the expert, which can then be used to retrain the DQN, and so on. The paper makes two contributions: (1) a new target for imitation learning, which is empirically shown to outperform a previously-suggested target and which results in the apprentice learning a policy of equal strength to the expert. COMMENTS: I found the paper generally well-written, clear and easy to follow, barring Section 6.

The paper investigates a minimax framework for statistical learning where the goal is to minimize the worst-case population risk over a family of distributions that are within a prescribed Wasserstein distance from the unknown data-generating distribution. The authors develop data-dependent generalization bound and data-independent excess risk bounds (using smoothness assumptions) in the setting where the classical empirical risk minimization (ERM) algorithm is replaced by a robust procedure that minimizes the worst-case empirical risk with respect to distributions contained in a Wasserstein ball centered around the data-generating empirical distribution. The statistical minimax framework investigated by the authors resembles in spirit the one introduced in [9], where the ambiguity set is defined via moment constraints instead of the Wasserstein distance. The paper is well-written, with accurate references to previous literature and an extensive use of remarks to guide the development of the theory. The contributions are clearly emphasized, and the math is solid.

Paper 1614 This paper studies the Kozachenko-Leonenko estimator for the differential entropy of a multivariate smooth density that satisfy a periodic boundary condition; an equivalent way to state the condition is to let the density be defined on the [0,1] d-torus. The authors show that the K-L estimator achieves a rate of convergence that is optimal up to poly-log factors. The result is interesting and the paper is well-written. I could not check the entirety of the proof but the parts I checked are correct. I recommend that the paper be accepted.

This paper studies the problem of dictionary selection, where the goal is to pick k vectors among a collection of n d-dimensional vectors such that these vectors can approximate T data points in a sparse representation. This problem is well-studied and the authors propose a new algorithm with theoretical guarantees which is faster than previous algorithms and which can handle more general constraints. This algorithm is based on a previous algorithm for the related problem of two stage submodular maximization called replacement greedy. It is first shown that replacement greedy also enjoys approximation guarantees for dictionary selection. Then, the authors further improve this algorithm to obtain replacement OMP, which is faster.

This paper considers the minimax estimation problem of neural net distance. The problem originates from the generative adversarial networks (GANs). In particular, the paper established the lower bound on the minimax estimation for neural net distance which seems to the first result of this kind. The authors then derived an upper bound on the estimation error which matches the minimax lower bound in terms of the order of sample size, and the norm of the parameter matrices. However, there is a gap of \sqrt{d} or \sqrt{d h} which remains as an open question.

This work uses best arm identification (BAI) techniques applies to the monte-carlo tree search problem with two-players (in a turn-based setting). The goal is to find the best action for player A to take by carefully considering all the next actions that player B and A can take in the following rounds. Access to a stochastic oracle to evaluate the values of leaves is supposed, hence the goal is to find approximately (with precision \epsilon) the best action at the root with high confidence (at least 1-\delta). Algorithms based on confidence intervals and upwards propagation (from leaf to the root) of the upper (for the MAX nodes, action by player A) and lower (for the MIN nodes, action by player B the opponent) confidence bounds are proposed. The algorithms are intuitive and well described, and well rooted in the fixed confidence BAI literature.

In this paper, authors explore the construction of meta-learning algorithms, through defining a viable search space and corresponding proxy tasks that are specifically designed and assessed for the task of dense prediction/semantic segmentation. The proposed method and the resulting network is tested on three different relevant datasets (Cityscapes, PASCAL VOC 12 and PASCAL person part). Main strengths: The method improves the state-of-the-art on three datasets including the competitive cityscapes and PASCAL VOC 2012. Most of the method ingredients (e.g. the proxy tasks) are well-thought-out and explored. The paper is fairly well-written and is easy to follow.

This paper presents a branch-and-bound based unified framework for piecewise linear neural network (PLNN) verification, and demonstrates how two existing methods (Reluplex and Planet) can be cast in these common terms. It explores other variations of various components of B-and-B, finding that a "smart branching (SB)" heuristic inspired by Kotler and Wong [12] results in a substantially faster method. My take on this paper is somewhat lukewarm, given the mix of strengths and weaknesses it has. STRENGTHS: The paper is very well-written, at least the first half of it. It motivates the problem well, sets the scope of the work (what it covers, what it doesn't), and summarizes the contributions in a meaningful way.