# Continuous Optimization for Feature Selection with Permutation-Invariant Embedding and Policy-Guided Search

arXiv: https://arxiv.org/abs/2505.11601 · HTML: https://mlsanity.com/paper/2505.11601/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Group-wise Reinforcement Feature Generation for Optimal and Explainable Representation Space Reconstruction](https://mlsanity.com/paper/2205.14526/) (2022)
- [Self-optimizing Feature Generation via Categorical Hashing Representation and Hierarchical Reinforcement Crossing](https://mlsanity.com/paper/2309.04612/) (2023)
- [Beyond Discrete Selection: Continuous Embedding Space Optimization for Generative Feature Selection](https://mlsanity.com/paper/2302.13221/) (2023)
- [Traceable Automatic Feature Transformation via Cascading Actor-Critic Agents](https://mlsanity.com/paper/2212.13402/) (2022)
- [Traceable Group-Wise Self-Optimizing Feature Transformation Learning: A Dual Optimization Perspective](https://mlsanity.com/paper/2306.16893/) (2023)
- [Feature Selection as Deep Sequential Generative Learning](https://mlsanity.com/paper/2403.03838/) (2024)
- [Unsupervised Generative Feature Transformation via Graph Contrastive Pre-training and Multi-objective Fine-tuning](https://mlsanity.com/paper/2405.16879/) (2024)
- [Reinforcement Feature Transformation for Polymer Property Performance Prediction](https://mlsanity.com/paper/2409.15616/) (2024)
- [Feature Interaction Aware Automated Data Representation Transformation](https://mlsanity.com/paper/2309.17011/) (2023)
- [MEL: Efficient Multi-Task Evolutionary Learning for High-Dimensional Feature Selection](https://mlsanity.com/paper/2402.08982/) (2024)

## Built on by (most cited first, 7 of 7)

- [Permutation-Invariant Representation Learning for Robust and Privacy-Preserving Feature Selection](https://mlsanity.com/paper/2510.05535/) (2025)
- [Hierarchical and Permutation-Invariant Feature Transformation Learning via Policy-Guided Embedding Search](https://mlsanity.com/paper/2609.10225/) (2026)
- [GPT-FT: An Efficient Automated Feature Transformation Using GPT for Sequence Reconstruction and Performance Enhancement](https://mlsanity.com/paper/2508.20824/) (2025)
- [Flat-Consensus Diffusion for Robust Data Reshaping under Noisy Evaluator](https://mlsanity.com/paper/2609.32696/) (2026)
- [Rethinking Data Augmentation under Covariate Shift: Invariant-Guided Diffusion and Prototype Reweighting](https://mlsanity.com/paper/2610.00873/) (2026)
- [Heterogeneous Multi-Agent Reinforcement Learning with Attention for Cooperative and Scalable Feature Transformation](https://mlsanity.com/paper/2511.21934/) (2025)
- [Which and When to Admit: Gradient Admission for Data-Centric Small Language Model Finetuning](https://mlsanity.com/paper/2610.07553/) (2026)

## Abstract (arXiv)

Feature selection removes redundant features to enhanc performance and computational efficiency in downstream tasks. Existing works often struggle to capture complex feature interactions and adapt to diverse scenarios. Recent advances in this domain have incorporated generative intelligence to address these drawbacks by uncovering intricate relationships between features. However, two key limitations remain: 1) embedding feature subsets in a continuous space is challenging due to permutation sensitivity, as changes in feature order can introduce biases and weaken the embedding learning process; 2) gradient-based search in the embedding space assumes convexity, which is rarely guaranteed, leading to reduced search effectiveness and suboptimal subsets. To address these limitations, we propose a new framework that can: 1) preserve feature subset knowledge in a continuous embedding space while ensuring permutation invariance; 2) effectively explore the embedding space without relying on strong convex assumptions. For the first objective, we develop an encoder-decoder paradigm to preserve feature selection knowledge into a continuous embedding space. This paradigm captures feature interactions through pairwise relationships within the subset, removing the influence of feature order on the embedding. Moreover, an inducing point mechanism is introduced to accelerate pairwise relationship computations. For the second objective, we employ a policy-based reinforcement learning (RL) approach to guide the exploration of the embedding space. The RL agent effectively navigates the space by balancing multiple objectives. By prioritizing high-potential regions adaptively and eliminating the reliance on convexity assumptions, the RL agent effectively reduces the risk of converging to local optima. Extensive experiments demonstrate the effectiveness, efficiency, robustness and explicitness of our model.