Accelerated Coordinate Descent with Arbitrary Sampling and Best Rates\n for Minibatches
Bibliographic record
Abstract
Accelerated coordinate descent is a widely popular optimization algorithm due\nto its efficiency on large-dimensional problems. It achieves state-of-the-art\ncomplexity on an important class of empirical risk minimization problems. In\nthis paper we design and analyze an accelerated coordinate descent (ACD) method\nwhich in each iteration updates a random subset of coordinates according to an\narbitrary but fixed probability law, which is a parameter of the method. If all\ncoordinates are updated in each iteration, our method reduces to the classical\naccelerated gradient descent method AGD of Nesterov. If a single coordinate is\nupdated in each iteration, and we pick probabilities proportional to the square\nroots of the coordinate-wise Lipschitz constants, our method reduces to the\ncurrently fastest coordinate descent method NUACDM of Allen-Zhu, Qu,\nRicht\\'{a}rik and Yuan.\n While mini-batch variants of ACD are more popular and relevant in practice,\nthere is no importance sampling for ACD that outperforms the standard uniform\nmini-batch sampling. Through insights enabled by our general analysis, we\ndesign new importance sampling for mini-batch ACD which significantly\noutperforms previous state-of-the-art minibatch ACD in practice. We prove a\nrate that is at most ${\\cal O}(\\sqrt{\\tau})$ times worse than the rate of\nminibatch ACD with uniform sampling, but can be ${\\cal O}(n/\\tau)$ times\nbetter, where $\\tau$ is the minibatch size. Since in modern supervised learning\ntraining systems it is standard practice to choose $\\tau \\ll n$, and often\n$\\tau={\\cal O}(1)$, our method can lead to dramatic speedups. Lastly, we obtain\nsimilar results for minibatch nonaccelerated CD as well, achieving improvements\non previous best rates.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.025 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".