Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence

Block coordinate descent (BCD) methods are widely-used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can lead to significantly faster BCD methods. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with a sparse dependency between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization

TK-KNN: A Balanced Distance-Based Pseudo Labeling Approach for Semi-Supervised Intent Classification

The ability to detect intent in dialogue systems has become increasingly important in modern technology. These systems often generate a large amount of unlabeled data, and manually labeling this data requires substantial human effort. Semi-supervised methods attempt to remedy this cost by using a model trained on a few labeled examples and then by assigning pseudo-labels to further a subset of unlabeled examples that has a model prediction confidence higher than a certain threshold. However, one particularly perilous consequence of these methods is the risk of picking an imbalanced set of examples across classes, which could lead to poor labels. In the present work, we describe Top-K K-Nearest Neighbor (TK-KNN), which uses a more robust pseudo-labeling approach based on distance in the embedding space while maintaining a balanced set of pseudo-labeled examples across classes through a ranking-based approach. Experiments on several datasets show that TK-KNN outperforms existing models, particularly when labeled data is scarce on popular datasets such as CLINC150 and Banking77. Code is available at https://github.com/ServiceNow/tk-knnComment: 9 pages, 6 figures, 4 table