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Improving Feasibility via Fast Autoencoder-Based Projections

Maria Chzhen, Priya L. Donti

Abstract

Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we propose a novel data-driven amortized approach that uses a trained autoencoder as an approximate projector to provide fast corrections to infeasible predictions. Specifically, we train an autoencoder using an adversarial objective to learn a structured, convex latent representation of the feasible set. This enables rapid correction of neural network outputs by projecting their associated latent representations onto a simple convex shape before decoding into the original feasible set. We test our approach on a diverse suite of constrained optimization and reinforcement learning problems with challenging nonconvex constraints. Results show that our method effectively enforces constraints at a low computational cost, offering a practical alternative to expensive feasibility correction techniques based on traditional solvers.

Improving Feasibility via Fast Autoencoder-Based Projections

Abstract

Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we propose a novel data-driven amortized approach that uses a trained autoencoder as an approximate projector to provide fast corrections to infeasible predictions. Specifically, we train an autoencoder using an adversarial objective to learn a structured, convex latent representation of the feasible set. This enables rapid correction of neural network outputs by projecting their associated latent representations onto a simple convex shape before decoding into the original feasible set. We test our approach on a diverse suite of constrained optimization and reinforcement learning problems with challenging nonconvex constraints. Results show that our method effectively enforces constraints at a low computational cost, offering a practical alternative to expensive feasibility correction techniques based on traditional solvers.

Paper Structure

This paper contains 14 sections, 10 equations, 2 figures, 12 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Fast Autoencoder-Based (FAB) Feasibility Improvement
  4. Two-phase autoencoder training
  5. Leveraging the trained feasibility mapping
  6. Experiments on Constrained Optimization Problems
  7. Experiments on Safety Gym (Safe RL)
  8. Conclusion
  9. Hyperparameters
  10. Constrained optimization hyperparameters
  11. Safety Gym hyperparameters
  12. Additional Experimental Results
  13. Additional Ablations and Configurations
  14. Statement on use of Large Language Models (LLMs)

Figures (2)

  • Figure 1: A schematic of FAB approximate projections. (1) Phase 1 of autoencoder training aims to enable reconstructions of the feasible set. (2) Phase 2 of autoencoder training introduces a discriminator (critic) to enable further structuring and refinement of the latent representation. (3) The trained autoencoder can be utilized as a plug-and-play attachment to another neural network model.
  • Figure 2: The nonconvex constraint sets tested in our constrained optimization settings, termed (from left to right): Blob with Bite, Concentric Circles, Star-Shaped, and Two Moons.