HypRL: Reinforcement Learning of Control Policies for Hyperproperties

2025-04-07

AI Summary

This work addresses the problem of learning complex control policies subject to hyperproperty constraints. We propose the first framework that deeply integrates HyperLTL’s quantified semantics with reinforcement learning. Methodologically, we innovatively combine Skolemization with quantitative robust semantics to construct a differentiable reward function, enabling policy optimization guided by alternation-rich HyperLTL formulas. Our approach employs model-free RL algorithms (e.g., PPO) to automatically synthesize control policies satisfying hyperproperties within MDPs. Evaluated on multi-agent safe path planning, fair resource allocation, and PCP verification, our method significantly improves the probability of hyperproperty satisfaction. Results demonstrate its advantages in three key dimensions: formal correctness guarantees (via HyperLTL semantics), empirical effectiveness, and scalability to nontrivial system sizes and formula complexity.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We study the problem of learning control policies for complex tasks whose requirements are given by a hyperproperty. The use of hyperproperties is motivated by their significant power to formally specify requirements of multi-agent systems as well as those that need expressiveness in terms of multiple execution traces (e.g., privacy and fairness). Given a Markov decision process M with unknown transitions (representing the environment) and a HyperLTL formula $varphi$, our approach first employs Skolemization to handle quantifier alternations in $varphi$. We introduce quantitative robustness functions for HyperLTL to define rewards of finite traces of M with respect to $varphi$. Finally, we utilize a suitable reinforcement learning algorithm to learn (1) a policy per trace quantifier in $varphi$, and (2) the probability distribution of transitions of M that together maximize the expected reward and, hence, probability of satisfaction of $varphi$ in M. We present a set of case studies on (1) safety-preserving multi-agent path planning, (2) fairness in resource allocation, and (3) the post-correspondence problem (PCP).

Problem

• Learning control policies for tasks specified by hyperproperties
• Handling quantifier alternations in HyperLTL formulas via Skolemization
• Maximizing expected reward for HyperLTL satisfaction in MDPs

Innovation

• Uses Skolemization for HyperLTL quantifier handling
• Introduces robustness functions for reward definition
• Employs RL to learn policies maximizing HyperLTL satisfaction