First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: This paper presents a provable guarantee under what conditions the convex optimization procedure (COP) can successfully recover the correct clustering solutions. The main result is: if the samples are drawn from two cubes, each being a cluster, then COP can obtain the correct clustering solution provided the distance between two cubes is larger than a threshold value that linearly depends on the cube size and the ratio of numbers of samples in each cluster. The proof is based on the idea of lifting, which projects the problem into a higher dimensional space that transforms the original formulation into a separable form (separating the regularization term into the sum of l_2 norm of each row). After constructing the optimal dual solution through some algebraic operations, the primal optimal solution can be obtained.

Neural Information Processing Systems http://nips.cc/

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper derives policy gradient algorithms for risk-sensitive MDPs for the particular criterion CVaR - a recent and popular criterion. First, the author derive gradients for the objective based on a Lagrangian relaxation of the constrained optimization. This naturally turns into a policy gradient algorithm where the expected return that appears in the gradient is estimated from full trajectories (reinforce-like). They then propose a scheme to obtain incremental actor-critic versions, where the critic computes the value (and other quantities) of an augmented MDP convenient for gradient estimation.

The empirical results are nice and the proposed method can be one of the candidates for the classification method for large datasets.

However, AdaMM is not suited for solving black-box optimization problems, where explicit gradient forms are difficult or infeasible to obtain. In this paper, we propose a zeroth-order AdaMM (ZO-AdaMM) algorithm, that generalizes AdaMM to the gradient-free regime.