First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper proposes a fairer optimization criterion, "regularized maximin", for centralized multi-agent MDPs. The idea, taken from the networking literature is elegant. The authors also propose an iterative optimization method that scales somewhat better than linear programming. The description of the transition model, lines 69-79, seems unnecessarily detailed.

We define a fairness solution criterion for multi-agent decision-making problems, where agents have local interests. This new criterion aims to maximize the worst performance of agents with a consideration on the overall performance. We develop a simple linear programming approach and a more scalable game-theoretic approach for computing an optimal fairness policy. This game-theoretic approach formulates this fairness optimization as a two-player zero-sum game and employs an iterative algorithm for finding a Nash equilibrium, corresponding to an optimal fairness policy.

Hessian of the population risk can have zero eigenvalues.

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Originality A major contribution of the paper is posing image set summarization as a submodular optimization problem; to the knowledge of this reviewer, this is a novel view of the problem. Together with a new dataset and the adaptation of ROUGE to a significantly different application domain, this paper has several novel contributions to the state of the art. Significance According to this reviewer, this work fits well in the topics of interest for NIPS, to which it makes a significant contribution. Q2: Please summarize your review in 1-2 sentences The paper presents an elegant formulation of the problem of image collection summarization along with a new dataset and an evaluation metric.

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We sampled 100 GP prior functions from zero mean and unit variance. After realizing them, the prior functions are used to optimize via Bayesian optimization. All the experiments are implemented with [8]. Same as Appendix B.1, except that all the models were trained for 200 The other details are the same as in Appendix B.1. Seen classes (0-9) Unseen classes (10-46) t -noise CE sharpness CE Sharpness CE Sharpness CNP 0.448 We also measure the sharpness [10] which essentially is a average prediction variance.

Stochastic classifiers arise in a number of machine learning problems, and have become especially prominent of late, as they often result from constrained optimization problems, e.g. for fairness, churn, or custom losses.