Conditional Policy Generator for Dynamic Constraint Satisfaction and Optimization

2025-09-21

AI Summary

This paper addresses constraint satisfaction and optimization problems with statistically independent variables in dynamic environments. We propose a reinforcement learning–based conditional policy generation method. Our key contributions are threefold: (i) We introduce the conditional generative adversarial network paradigm to dynamic constrained optimization for the first time, enabling multimodal solution distribution modeling conditioned on environmental constraints; (ii) we integrate static prior knowledge with dynamic constraint feedback to construct a policy learning framework that balances stability and adaptability; and (iii) we incorporate noise-prior sampling, differentiable reward design, and maximum-likelihood supervised updates to support online adaptation to evolving constraints. Experiments on multimodal constrained tasks demonstrate that our conditional policy significantly outperforms unconditional baselines, achieving simultaneous improvements in solution feasibility and diversity.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Leveraging machine learning methods to solve constraint satisfaction problems has shown promising, but they are mostly limited to a static situation where the problem description is completely known and fixed from the beginning. In this work we present a new approach to constraint satisfaction and optimization in dynamically changing environments, particularly when variables in the problem are statistically independent. We frame it as a reinforcement learning problem and introduce a conditional policy generator by borrowing the idea of class conditional generative adversarial networks (GANs). Assuming that the problem includes both static and dynamic constraints, the former are used in a reward formulation to guide the policy training such that it learns to map to a probabilistic distribution of solutions satisfying static constraints from a noise prior, which is similar to a generator in GANs. On the other hand, dynamic constraints in the problem are encoded to different class labels and fed with the input noise. The policy is then simultaneously updated for maximum likelihood of correctly classifying given the dynamic conditions in a supervised manner. We empirically demonstrate a proof-of-principle experiment with a multi-modal constraint satisfaction problem and compare between unconditional and conditional cases.

Problem

• Solves constraint satisfaction in dynamically changing environments
• Handles problems with both static and dynamic constraints
• Uses conditional policy generator for statistical independence variables

Innovation

• Uses conditional policy generator with GAN concept
• Frames dynamic constraint satisfaction as reinforcement learning
• Encodes dynamic constraints as class labels for conditioning