Additional Feedback: Post Rebuttal: Authors have addressed all the questions about the theoretical contributions. I encourage authors to strengthen the experiments with real data and baselines. The Preliminaries section just mentions that the clustering C is consistent with W. W is just defining the distance between every pair of points. Assuming it induces a seminorm does not decide the optimization objective to construct C. Are we considering k-means objective under d_W metric? Or are we assuming that the clusters can be arbitrary but the points form ellipsoid according to a W that satisfies gamma margin? Please clarify if I am correct.

I have consequently increased my score. The paper proposes to decompose the parameters into L distinct parameter blocks. Each of these blocks is seen as solving a "pseudo-task", learning a linear map from inputs to outputs. The parameters of these blocks are generated by K hypermodules (small hypernetworks) that condition on a context vector for each pseudo-task based. The alignment of hypermodules to pseudo-tasks is governed by a softmax function and learned during training similar to mixture-of-experts.

I'm glad you commented on the learning rate selection, because this was a major point of our discussion. The main reason I can't increase my score is that many definitions, explanations and experiment details are missing, making it extremely hard to evaluate the real value of your experiments. This was additionally complicated by the fact that you didn't provide your code when submitting the paper. I hope that you will do a major revision, for example include a section in supplementary material with all experiments details. Just in case, here are my suggestions for some extra experiments: 1. Measure and plot the effect of data augmentation on bias of the gradient.

This manuscript proposes a novel method for Bayesian batch active learning through sparse subset approximation and a convenient set of reductions to arrive at a tractable algorithm. This method is validated and explored through a series of special cases (linear regression and classification), illustrations, and experiments. Overall the method appears to be competitive with the state of the art. Overall this manuscript is well written, insightful, and enjoyable to read. The proposed approach outlined on page 3 is elegant, appears to work well in practice, and the approach may be useful in other settings.

Summary: The main points in the paper are: -- expected reward objective has exponentially many local maxima -- smooth risk and hence, the new loss L(q, r, x) which are both calibrated can be used and L is strongly convex implying a unique global optimum. Originality: The work is original. Clarity: The paper is clear to read, except some details in the experimental section, on page 4, where the meanings of the risk R(\pi) is not described clearly. Significance and comments: First, in the new objective for contextual bandits, the authors mention that this objective is not the same as the trust-region or proximal objectives used in RL (line 237), but how does this compare with the maximum entropy RL (for example, Harrnoja et.al, Soft Q-learning and Soft actor-critic) objectives with the same policy and value function/reward models? In these maxent RL formulations, an estimator similar to Eqn 12, Page 5 is optimized.

This paper introduces a new coreset construction mechanism for fair clustering in which the points can be of multiple disjoint types. As in classic fair clustering, the goal of this work is to construct a clustering in which the types represented in each cluster are balanced. Unlike previous work, the focus here is on constructing the clustering efficiently via coresets. This work provides a coreset construction algorithm for fair k-median (previously unknown) and improves the previously known coreset construction algorithm for fair k-means. In addition to theoretical contributions with respect to coreset size and construction time, the authors also provide a small empirical study.

This paper proposes a new MCTS algorithm, Maximum Entropy for Tree Search (MENTS), which combines the maximum entropy policy optimization framework with MCTS for more efficient online planning in sequential decision problems. The main idea is to replace the Monte Carlo value estimate with the softmax value estimate as in the maximum entropy policy optimization framework, such that the state value can be estimated and back-propagated more efficiently in the search tree. Another main novelty is that it proposes an optimal algorithm, Empirical Exponential Weight (E2W), to be the tree policy to do more exploration. It shows that MENTS can achieve an exponential convergence rate towards finding the optimal action at the root of the tree, which is much faster than the polynomial convergence rate of the UCT method. The experimental results also demonstrate that MENTS performs significantly better than UCT in terms of sample efficiency, in both synthetic problems and Atari games.

This paper presents an appealing idea to combine current max-entropy methods in RL with Monte-Carlo Tree Search. A theoretical result shows improved rate of convergence, while empirical results show improved sample efficiency. The initial reviews were quite positive; I only noted a small number of issues mentioned in the reviews of R1 and R3. In our discussions after reading the author feedback, R3 noted that some of his concerns have not been addressed. R2 replied, saying that these concerns are relatively minor and can be addressed in the final version.

Post-rebuttal response: I read the authors' response and don't have any further comments. This paper considers the model of "robust statistics" where an alpha fraction of the training data comes from the ground truth distribution while the rest are corrupted arbitrarily (i.e. Traditionally, research has been on the setting where alpha is large, so that the parameters of the true distribution are information-theoretically identifiable. However, recent focus has been on the small alpha setting. Here, the parameters of the true distribution cannot be uniquely identified even with infinitely many samples.

This paper studies the challenging problem of doing linear regression in the setting where an overwhelming fraction (1-alpha) of the examples are adversarially corrupted. It extends recent work on using the Sum-of-Squares hierarchy for robust estimation. The main contribution is realizing that anti-concentration (and being able to certify anti-concentration) is the key. The algorithm has a high running time (d (1/alpha 8)) but given the challenging nature of the problem, the reviewers felt that the fact that the problem can be solved in polynomial time for any fixed alpha 0 is surprising and an important contribution.