arXiv：cs.LG· Adam Bos\'ak, Andrii Kliachkin, Gilles Bareilles, Allen Gehret, Allahkaram Shafiei, Jana Lep\v{s}ov\'a, Jakub Mare\v{c}ek·· 7 小时前AI 评分34
随机惩罚-障碍法 SPBM：面向约束机器学习的新优化方法
Stochastic Penalty-Barrier Method for Constrained Machine Learning
AI 导读
研究者提出随机惩罚-障碍法（SPBM），通过双变量指数平均、稳定化惩罚调度和 Moreau 包络处理非光滑性，扩展了经典惩罚与障碍方法。在多组公平性与物理信息神经网络实验中，SPBM 与当前最优方法表现相当。公平性基准显示，当约束数量从 90 增至 9900 时，约束机器学习方法的每 epoch 运行时间基本与约束数量无关，且不超过正则化 Adam 的 1.3 倍。
正文
Abstract:Constrained Machine Learning (CML) enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. In this work, we introduce the Stochastic Penalty-Barrier Method (SPBM) for CML problems. SPBM extends classical penalty and barrier methods by incorporating an exponential averaging of the dual variables, a stabilized penalty schedule, and the Moreau envelope to handle non-smoothness. We analyze the bias that mini-batching introduces in the barrier function and show that the feasible set of the resulting transformed problem is contained within the original one. We compare SPBM with CML baselines across multiple fairness and physics informed neural networks experiments. We find that SPBM is competitive with state-of-the-art methods. We also observe, on our fairness-based computational benchmark, that the per-epoch runtime of CML methods is largely independent of the number of constraints, and within $1.3\times$ of the per-epoch runtime of regularized Adam, for a number of constraints ranging from $90$ to $9900$.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.18618 [cs.LG] |
| (or arXiv:2605.18618v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.18618 arXiv-issued DOI via DataCite |
Submission history
From: Adam Bosák [view email]
[v1]
Mon, 18 May 2026 16:26:26 UTC (7,574 KB)
[v2]
Tue, 19 May 2026 17:03:47 UTC (7,574 KB)
[v3]
Tue, 6 Oct 2026 13:29:18 UTC (4,331 KB)
来源：arXiv：cs.LG · arxiv.org