发表机构
Elmore Family School of Electrical and Computer Engineering, Purdue University（普渡大学埃尔莫尔电气与计算机工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对基于VAE的约束优化的三个挑战，提出多阶段约束优化框架MCOF，通过结合EC-VAE、UT模块、CPFM等方法，在潜在空间有效采样、识别有效决策变量并执行约束，经合成问题和药物设计任务验证了该框架的有效性。
AI 中文摘要
变分自编码器（VAE）将高维、常含噪声的数据转换为紧凑的潜在表示，使下游优化更易处理。基于VAE的约束优化存在三个挑战：在潜在空间内有效采样；识别实际影响目标和约束的有效决策变量；在不破坏训练的情况下执行约束。我们提出了多阶段约束优化框架（MCOF）。首先，将熵约束VAE（EC-VAE）与特征选择器相结合，将目标和约束信息嵌入到潜在变量的指定子集中。其次，统一变换（UT）模块应用逐维概率积分变换。然后，约束优先级过滤方法（CPFM）通过在过滤接受测试下交替减少违规和减少目标步骤来解决替代问题。最后，对未选择的潜在坐标重新采样以生成单个优化解决方案的不同解码。我们在一个合成问题和ZINC250k药物设计任务上验证了MCOF。
英文摘要
Variational autoencoders (VAEs) transform high-dimensional, often noisy data into a compact latent representation, making downstream optimization more tractable. Three challenges persist in VAE-based constrained optimization: (i) sampling effectively within the latent space, (ii) identifying the active decision variables that actually influence the objective and constraints, and (iii) enforcing constraints without destabilizing training. We propose a Multi-stage Constrained Optimization Framework (MCOF). First, an entropy-constrained VAE (EC-VAE) coupled with a feature selector embeds objective and constraint information into a designated subset of latent variables, so that optimization proceeds over a low-dimensional subspace while the remaining coordinates supply solution diversity. Second, a Uniform Transformation (UT) module applies a per-dimension probability integral transform, replacing the irregular aggregate posterior with a uniform distribution over a bounded box and mitigating posterior collapse and Gaussian mixture bias. Third, a constraint-priority filter method (CPFM) solves the resulting surrogate problem by alternating violation-reduction and objective-reduction steps under a filter acceptance test, returning solutions that are feasible for the learned surrogate to a specified tolerance without requiring multiplier estimation. Finally, unselected latent coordinates are resampled to generate diverse decodings of a single optimized solution. We validate MCOF on a synthetic problem, where we ablate each stage and recover the analytic optimum, and on a ZINC250k drug design task, where the generated molecules satisfy the imposed constraints and are entirely novel relative to the training set.
Comments14 pages, 10 figures, 6 tables, 3 algorithms. Preprint
