Paper:
Efficient Use of Limited-Memory Accelerators for Linear Learning on Heterogeneous Systems
We propose a generic algorithmic building block to accelerate training of machine learning models on heterogeneous compute systems. Our scheme allows to efficiently employ compute accelerators such as GPUs and FPGAs for the training of large-scale machine learning models, when the training data exceeds their memory capacity. Also, it provides adaptivity to any system's memory hierarchy in terms of size and processing speed. Our technique is built upon novel theoretical insights regarding primal-dual coordinate methods, and uses duality gap information to dynamically decide which part of the data should be made available for fast processing. To illustrate the power of our approach we demonstrate its performance for training of generalized linear models on a large-scale dataset exceeding the memory size of a modern GPU, showing an order-of-magnitude speedup over existing approaches.

Review:
The paper presents a specific way of exploiting a system with two heterogeneous compute nodes with complementary capabilities. The idea is to perform block co-ordinate algorithm with the subproblem of optimizing with the block variables solved at the node with high-compute-low-memory and the subproblem of choosing the block at the node with low-compute-high-memory.
Here are some comments:
1. Overall, it is not very clear why the above is the only worthwhile strategy to try. Atleast empirical comparison with popular distributed algorithms (that ignore the resource capabilities) is necessary in order to access the merit of this proposal.
2. More importantly, the proposed split-up of workload in inherently not parallelizable. Hence a time-delay strategy is employed. Though empirically it is shown that it works, it not clear why this is the way to go?
3. In literature of block co-ordinate descent scoring functions (similar to (6) ) are popular. An empirical comparison with strategies like those used in SMO (libsvm etc.; first order and second order criteria for sub-optimality) seems necessary.
4. The results of Theorem1 and Theorem2 are interesting (I have not been able to fully check the correctness of the proofs).
5. Refer eqn (2). The duality is lower-bounded by the expression on LHS in (2). It is need not be equal to it.  
I have read the rebuttal and would like to stay with the score.