First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes an approach to stochastic multi-objective optimization. The main idea is simply described: optimize a single objective while taking other objectives as constraints. The authors proposes a primal-dual stochastic optimization algorithm to solve the problem and prove that it achieves (for the primal objective) the optimal 1/\sqrt{T} convergence rate. As far as I am concerned, the theory is solid and it does provide a good insight into the problem of interest.

Due to state transitions, it is challenging to balance the contribution from each dimension for achieving near-optimality.

We consider the problem of fitting variational posterior approximations using stochastic optimization methods.

We consider the problem of fitting variational posterior approximations using stochastic optimization methods.

We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. It presents a slight modification of the NAC algorithm, where the original algorithm is a special case which is called forgetful NAC. The authors show that forget full Nac and optimistic policy iteration are equivalent. The authors also present a non-optimality result for soft-greedy Gibbs distribution, I.e., the optimal solution is not a fixed point of the policy iteration algorithm. I liked the unified view on both type of algorithms.

The authors propose an efficient scheme to solve LP relaxations of combinatorial optimization problems. Their contribution is a novel scheme and analysis that takes into account the original goal of constructing an integral feasible solution from the relaxed solution. They prove that an approximate solution is sufficient to construct an integral alpha-approximate solution to the vertex cover problem. They also prove a convergence result for an algorithm solving a suitably constructed QP approximation to a general standard form LP problem. The proposed method is evaluated experimentally on a number of combinatorial optimization problems and shown to be competitive with Cplex, a state-of-the-art LP solver.

Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning.

The Frank-Wolfe algorithm is a classic method for constrained optimization problems.