Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods, our proposed methods only require O(1) operations in each iteration. We also develop a variance-reduction variant of the algorithm that converges linearly. Numerical experiments suggest that our methods are faster than existing ones such as proximal SGD, SVRG and SAGA on high-dimensional problems.

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

I have decided not to increase my grade since my criticism on intuition & readability and time plots really depends on the quality of the re-write and the plots. In the rebuttal the authors have suggested that their method can be deduced using a saddle point formulation and they will include time plots, which I look forward to seeing. But still, it depends on the re-write. Furthermore on why I feel I cannot raise my grade, as pointed out by Reviewer 1, an application where data access is truly the bottleneck (such as a distributed setting) would be very welcome and would result in an excellent and well rounded paper i.e. good theoretical results, and a good practical result. This is the first time I've seen a O(1) per iteration cost, and thus I find the paper quite interesting in the regime where loading data is truly the bottleneck. On the downside, very little intuition or any form of a derivation of the algorithms is offered, making the paper only suitable for experts in convex optimization and proximal methods.

Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods, our proposed methods only require O(1) operations in each iteration. We also develop a variance-reduction variant of the algorithm that converges linearly. Numerical experiments suggest that our methods are faster than existing ones such as proximal SGD, SVRG and SAGA on high-dimensional problems.

We study the problem of learning policy of an infinite-horizon, discounted cost, Markov decision process (MDP) with a large number of states. We compute the actions of a policy that is nearly as good as a policy chosen by a suitable oracle from a given mixture policy class characterized by the convex hull of a set of known base policies. To learn the coefficients of the mixture model, we recast the problem as an approximate linear programming (ALP) formulation for MDPs, where the feature vectors correspond to the occupation measures of the base policies defined on the state-action space. We then propose a projection-free stochastic primal-dual method with the Bregman divergence to solve the characterized ALP. Furthermore, we analyze the probably approximately correct (PAC) sample complexity of the proposed stochastic algorithm, namely the number of queries required to achieve near optimal objective value. We also propose a modification of our proposed algorithm with the polytope constraint sampling for the smoothed ALP, where the restriction to lower bounding approximations are relaxed. In addition, we apply the proposed algorithms to a queuing problem, and compare their performance with a penalty function algorithm. The numerical results illustrates that the primal-dual achieves better efficiency and low variance across different trials compared to the penalty function method.

Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods, our proposed methods only require O(1) operations in each iteration. We also develop a variance-reduction variant of the algorithm that converges linearly. Numerical experiments suggest that our methods are faster than existing ones such as proximal SGD, SVRG and SAGA on high-dimensional problems.

Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods, our proposed methods only require O(1) operations in each iteration. We also develop a variance-reduction variant of the algorithm that converges linearly. Numerical experiments suggest that our methods are faster than existing ones such as proximal SGD, SVRG and SAGA on high-dimensional problems.