Strategy/projects/files/splitting/splitting_optima2026_submission.md
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splitting_optima2026_submission

Splitting Paper — OPTIMA 2026 Submission Package

Target: OPTIMA 2026 (Optimization and Applications, Springer LNCS)
Dates: 22–26 September 2026, Petrovac, Budva, Montenegro
CFP status: дедлайны не опубликованы (апрель 2026); ожидается ~май (abstract), ~июнь (full)
Format: 10–15pp LNCS (conference short version of JCAM 29pp)
Grant: РНФ 23-11-00229-П — уточнить участие у Матюхина!

Title

“Stochastic Gradient Algorithms from ODE Splitting Perspective”

(авторы: Daniil Merkulov, Ivan Oseledets — Skoltech)

Conference Abstract (150 words, LNCS style)

We present a unified framework for stochastic gradient methods through the lens of operator splitting for gradient-flow ODEs. We show that one epoch of SGD is precisely a first-order Lie–Trotter splitting of the gradient-flow ODE, derive an upper bound on the global splitting error, and establish that the Kaczmarz (ART) method is the exact limiting case of unit-batch SGD for the linear least-squares problem. Replacing the standard Euler step by a higher-order local ODE solver yields a splitting optimisation scheme that is markedly more robust to step-size choice across linear, logistic, and softmax regression benchmarks. For the LASSO ($\ell_2 + \ell_1$) objective, we analyse both the first-order Lie–Trotter (ISTA) and second-order Strang splitting: the first-order scheme achieves zero asymptotic bias, whereas the Strang scheme incurs a bias floor scaling as $O(h^2\lambda^2)$. A support-characterisation conjecture for Strang-ISTA fixed points is proposed and confirmed numerically.

Keywords: stochastic gradient descent, operator splitting, Lie–Trotter, ODE methods, LASSO, ISTA, Kaczmarz method

LNCS Highlights (4 bullets — required)

  • SGD reinterpreted as Lie–Trotter operator splitting of the gradient-flow ODE
  • Higher-order local ODE solvers yield step-size-robust splitting optimisation scheme
  • Kaczmarz method is the exact unit-batch splitting limit for linear least squares
  • LASSO: Lie–Trotter ISTA achieves zero bias; Strang-ISTA has $O(h^2\lambda^2)$ bias floor

Proposed LNCS Short Version Structure (10–12pp)

Section Pages Content
1. Introduction 1.5 Problem motivation, contributions
2. SGD as Splitting Scheme 2 Lie–Trotter derivation, Table 1
3. Global Splitting Error 1 Theorem + bound
4. Kaczmarz as Exact Limit 1.5 Proposition + proof sketch
5. LASSO Analysis 2.5 LT-ISTA vs Strang-ISTA, bias floor, Conjecture C
6. Experiments 1.5 lin.reg + logistic + softmax (2 figures)
7. Conclusion 0.5
References 1 ~15 refs

Source: collapse §§2–5 of JCAM paper; keep all 4 main results; drop extended proofs → appendix or arXiv

Action Plan

  1. Даниил: подтвердить у Матюхина — в гранте РНФ 23-11-00229-П?
  2. Следить: conf-optima.ru еженедельно — ждать появления CFP/дедлайнов
  3. Как только CFP появится: начать LNCS версию (~2-3 дня работы)
    - Сократить JCAM 29pp → 10-12pp LNCS
    - Оставить: Theorem (splitting error bound), Proposition (Kaczmarz), Theorem (Strang-ISTA bias)
    - Убрать: расширенные доказательства, §§ с Conjecture B (оставить C)
  4. arXiv preprint: выложить текущий JCAM черновик до дедлайна OPTIMA

Review Item (для Даниила)

Вопрос: Подтвердить участие в гранте РНФ 23-11-00229-П у Матюхина — нужно ли готовить OPTIMA 2026 submission?

  • Если ДА: начинаем LNCS версию как только выйдет CFP (~май)
  • Если НЕТ: рассмотреть другую конференцию (AIJourney ~июль)

Подготовлено: Феанор worker 17:05 MSK 9 апр 2026

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