Towards Reliable Neural Optimizers: A Permutation Equivariant Neural Approximation for Information Processing Applications

TL;DR

This work tackles real-time optimization in dynamic sensor networks typical of Dynamic Data Driven Applications Systems (DDDAS) by introducing LOOP-PE, a permutation-equivariant neural approximator. The model combines an Optimality Module with a Self-Attention-based embedding and a Feasibility Module that uses a generalized gauge map via LOOP-LC2.0 to convert virtual predictions into feasible actions while respecting local and coupled constraints. Empirical results in a Virtual Power Plant setting show LOOP-PE achieves near-optimal solutions with zero feasibility gaps and substantially faster runtimes than a commercial solver ($\text{GUROBI}$), demonstrating strong scalability to varying sensor counts and unordered data. These contributions advance robust, real-time decision-making for multi-sensor, heterogeneous data integrations in dynamic environments.

Abstract

The complexities of information processing across Dynamic Data Driven Applications Systems drive the development and adoption of Artificial Intelligence-based optimization solutions. Traditional solvers often suffer from slow response times and an inability to adapt swiftly to real-time input variations. To address these deficiencies, we will expand on our previous research in neural-based optimizers by introducing a machine learning-enabled neural approximation model called LOOP-PE (Learning to Optimize the Optimization Process -- Permutation Equivariance version). This model not only enhances decision-making efficiency but also dynamically adapts to variations of data collections from sensor networks. In this work, we focus on mitigating the heterogeneity issues of data collection from sensor networks, including sensor dropout and failures, communication delays, and the complexities involved in integrating new sensors during system scaling. The proposed LOOP-PE model specifically overcomes these issues with a unique structure that is permutation equivariant, allowing it to accommodate inputs from a varying number of sensors and directly linking these inputs to their optimal operational outputs. This design significantly boosts the system's flexibility and adaptability, especially in scenarios characterized by unordered, distributed, and asynchronous data collections. Moreover, our approach increases the robustness of decision-making by integrating physical constraints through the generalized gauge map method, which theoretically ensures the decisions' practical feasibility and operational viability under dynamic conditions. We use a DDDAS case study to demonstrate that LOOP-PE model reliably delivers near-optimal and adaptable solutions, significantly outperforming traditional methods in managing the complexities of multi-sensor environments for real-time deployments.

Figures (3)

• Figure 1: Illustration of the Permutation Equivariance Property in the Real-Time Management Optimizer. This feature ensures output corresponds to input order, enabling adaptability to sensor addition or removal without extensive reconfiguration.
• Figure 2: Building blocks of the proposed $\mathcal{LOOP-PE}$ model. The Optimality Module uses an attention mechanism to process input from varying sensor numbers and generate virtual predictions. The Feasibility Module uses the $\mathcal{LOOP-LC}\space2.0$ model ref_article_8 to convert these predictions into practical, constraint-compliant actions, ensuring flexibility and robustness across different sensor setups and dynamics.
• Figure 3: Solution spectrum for various test samples using data from multiple sensors. This figure displays the solution spectra obtained from different sensors, illustrating the $\mathcal{LOOP-PE}$ method's performance across diverse conditions. The ability to accept input in any order makes the model more adaptable to changes in the data collection setup, enhancing its flexibility and robustness in dynamic environments.