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HypRL: Reinforcement Learning of Control Policies for Hyperproperties

Tzu-Han Hsu, Arshia Rafieioskouei, Borzoo Bonakdarpour

TL;DR

HypRL introduces a specification-guided reinforcement learning framework for multi-agent systems by leveraging HyperLTL hyperproperties to express relational objectives and constraints. It tackles quantifier alternations with Skolemization, and replaces Boolean satisfaction with quantitative robustness as the reward signal, enabling off-the-shelf RL to maximize the probability of satisfying the hyperproperty. A three-step pipeline—Skolemization, robustness-based semantics, and RL training—learns a tuple of policies that jointly satisfy the HyperLTL specification. Empirical results across SRL, DST, PCP, and wildfire scenarios demonstrate that HypRL outperforms baselines and can handle complex, relational objectives that are difficult for traditional reward designs.

Abstract

Reward shaping in multi-agent reinforcement learning (MARL) for complex tasks remains a significant challenge. Existing approaches often fail to find optimal solutions or cannot efficiently handle such tasks. We propose HYPRL, a specification-guided reinforcement learning framework that learns control policies w.r.t. hyperproperties expressed in HyperLTL. Hyperproperties constitute a powerful formalism for specifying objectives and constraints over sets of execution traces across agents. To learn policies that maximize the satisfaction of a HyperLTL formula $φ$, we apply Skolemization to manage quantifier alternations and define quantitative robustness functions to shape rewards over execution traces of a Markov decision process with unknown transitions. A suitable RL algorithm is then used to learn policies that collectively maximize the expected reward and, consequently, increase the probability of satisfying $φ$. We evaluate HYPRL on a diverse set of benchmarks, including safety-aware planning, Deep Sea Treasure, and the Post Correspondence Problem. We also compare with specification-driven baselines to demonstrate the effectiveness and efficiency of HYPRL.

HypRL: Reinforcement Learning of Control Policies for Hyperproperties

TL;DR

HypRL introduces a specification-guided reinforcement learning framework for multi-agent systems by leveraging HyperLTL hyperproperties to express relational objectives and constraints. It tackles quantifier alternations with Skolemization, and replaces Boolean satisfaction with quantitative robustness as the reward signal, enabling off-the-shelf RL to maximize the probability of satisfying the hyperproperty. A three-step pipeline—Skolemization, robustness-based semantics, and RL training—learns a tuple of policies that jointly satisfy the HyperLTL specification. Empirical results across SRL, DST, PCP, and wildfire scenarios demonstrate that HypRL outperforms baselines and can handle complex, relational objectives that are difficult for traditional reward designs.

Abstract

Reward shaping in multi-agent reinforcement learning (MARL) for complex tasks remains a significant challenge. Existing approaches often fail to find optimal solutions or cannot efficiently handle such tasks. We propose HYPRL, a specification-guided reinforcement learning framework that learns control policies w.r.t. hyperproperties expressed in HyperLTL. Hyperproperties constitute a powerful formalism for specifying objectives and constraints over sets of execution traces across agents. To learn policies that maximize the satisfaction of a HyperLTL formula , we apply Skolemization to manage quantifier alternations and define quantitative robustness functions to shape rewards over execution traces of a Markov decision process with unknown transitions. A suitable RL algorithm is then used to learn policies that collectively maximize the expected reward and, consequently, increase the probability of satisfying . We evaluate HYPRL on a diverse set of benchmarks, including safety-aware planning, Deep Sea Treasure, and the Post Correspondence Problem. We also compare with specification-driven baselines to demonstrate the effectiveness and efficiency of HYPRL.

Paper Structure

This paper contains 60 sections, 2 theorems, 51 equations, 13 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Contributions:
  3. Related Work
  4. Logic-based Single-agent RL.
  5. Logic-based Multi-Agent Reinforcement Learning.
  6. Shield Synthesis.
  7. Preliminaries
  8. Markov Decision Processes (MDP).
  9. Finite Semantics for HyperLTL.
  10. Example.
  11. Problem Statement
  12. Example.
  13. Algorithmic Details of HypRL
  14. Step 1: HyperLTL Skolemization
  15. Step 2: Policy Learning with Quantitative Semantics
  16. ...and 45 more sections

Key Result

Theorem 1

Given an MDP $\mathcal{M}$ and a HyperLTL formula $\varphi$, an optimal tuple of policies $\langle \pi^{\star}_i \rangle_{i \in {\mathds{\mathds{Q}}^\exists_{}}} {\cup}_{{\leq}} \langle \pi^{\star}_j \rangle_{j \in {\mathds{\mathds{Q}}^\forall_{}}}$ for $\mathbf{Skolem}(\varphi)$ is also an optima

Figures (13)

  • Figure 1: A wildfire scenario with two objectives ($O_1$, $O_2$) and two relational constraints ($C_1$, $C_2$).
  • Figure 2: The MDP of The grid-world in \ref{['fig:motivation']}.
  • Figure 3: Quantitative semantics for LTL.
  • Figure 4: Overview of HypRL.
  • Figure 5: PCP results, avg. and std. error of total matches, 10 runs.
  • ...and 8 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2