Title: HypRL: Reinforcement Learning of Control Policies for Hyperproperties
Venue: NeurIPS 2025
Accepted: yes
Keywords: Reinforcement learning

formal methods

hyperproperties

temporal logics

specification-based RL

multi-agent RL

reward shaping

HyperLTL

MDP
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 $\varphi$, 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 $\varphi$. 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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel formal specification guided multi-agent reinforcement learning (MARL) framework where specifications are given as hyperproperties. In particular, they adopt the HyperLTL logic which extends LTL with existential and universal quantifiers over  traces. The authors claim that HyperLTL, in the context of MARL, allows greater flexibility in specifying interdependencies between agent behaviors using quantifier alternations and they demonstrate this with a relevant example. Their method involves first considering a Skolemized version of the specification and using some quantitative semantics of LTL as a reward to train off-the-shelf RL algorithms that gives a centralized policy producing actions for all the agents. They implement their method and test it on three discrete environments.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\nThe introduction of hyperproperties in the context of multi-agent reinforcement learning has not been explored before to the best of our knowledge so this is indeed a novel direction.\n\nWeaknesses\nFirstly, we believe that the problem statement and the benchmarks used do not show the utility of using hyperproperties. In the current formulation of the problem statement (page 4), it is unclear what is the role of the quantifier alternation because it is trying to maximize the probability that a tuple of traces sampled from the agents' policies together satisfy the specification. In particular, this probability is not dependent on the quantifiers in the specification.\n \nConsider the case of the motivating example used in the introduction. Here, we could define the same specification as an LTL formula over a zipped trace of the firefighter and medical agents and the problem statement would remain the same. This is also the case with all the other benchmark specifications that are considered. In fact, the final policy produced also does not depend on the quantifiers since it is a centralized policy that predicts actions simultaneously for all the agents.  \n\nTo make this more concrete, if we fix the policies for all the agents, then we can resolve the MDP into a Markov chain for each agent. Then the quantifier-free LTL part of the specifications presented in this paper can be seen as an LTL formula over the product of these Markov chains. So these specifications do not define hyperproperties over this product Markov chain. In other words, interdependence between traces in the Markov chains of each agent specified with an LTL formula is not a hyperproperty. Furthermore, if we did want to consider hyperproperties over the product, it is unclear whether HyperLTL has well defined probabilistic semantics over a Markov chain. We refer to Abraham and Bonakdarpour [1] and Dimitrova et al [2] who define different probabilistic temporal logics to specify hyperproperties over Markov chains and MDPs respectively.\n\nThe above problem is accompanied by a lack of a sound and complete formalization. Despite multi-agent reinforcement learning being the focus of the paper, the initial definitions do not specify these multiple agents and how their traces are represented in the MDP. Next, in the definition of the semantics of HyperLTL, it is stated that a tuple of traces $\\mathcal{T}$ satisfies the specification $\\forall \\pi.\\phi$, if for all $t\\in \\mathcal{T}$, $(\\mathcal{T}, \\Pi[\\pi \\to t]) \\models \\phi$, which means that $\\phi$ is satisfied by all assignments of traces to $\\pi$. However, in the remainder of the paper, the convention seems to arbitrarily shift to being such that the tuple of traces $\\mathcal{T}$ represents a sequence of assignments for the quantified variables in the formula. This again seems to point to the fact that the quantifiers play no role.\n\nFinally, the proposed training procedure does not present any novel insights since it uses off-the-shelf RL algorithms with rewards given by quantitative semantics of the LTL formula and only trains a centralized policy that controls all the agents at the same time. Essentially, the multi-agent control problem is turned into a single-agent control problem.\n\n[1] E. Abraham and B. Bonakdarpour. HyperPCTL: A temporal logic for probabilistic hyperproperties. In Quantitative Evaluation of Systems, QEST 2018, Proc., 2018.\n\n[2] Rayna Dimitrova, Bernd Finkbeiner, Hazem Torfah. Probabilistic Hyperproperties of Markov Decision Processes. In ATVA 2020.\n\nQUESTIONS:\nMy main confusion is about the problem formalization and problem statement. If we have just a single MDP, what does it mean to synthesize multiple policies? How does the quantifier alternation affect optimization?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-27"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes HypRL, a reinforcement learning framework that learns multi-agent control policies guided by specifications written in HyperLTL, a logic for expressing properties over multiple execution traces. Unlike traditional approaches that rely on manually crafted rewards, HypRL derives reward signals from logical robustness values, enabling it to handle complex relational constraints between agents.\n\nThe framework uses Skolemization to manage quantifier alternation in HyperLTL and trains policies using standard RL algorithms. Evaluations across tasks like Deep Sea Treasure, and the Post Correspondence Problem show that HypRL significantly outperforms standard RL baselines.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- [S1] The wildfire scenario offers an intuitive and accessible introduction to the problem and why standard reward shaping fails.\n- [S2] The method uses HyperLTL and Skolemization to define a novel, theoretically grounded framework for learning multi-agent policies under complex constraints.\n- [S3] The paper avoids ad hoc reward engineering by using logical robustness values as a principled reward signal.\n\n## Weaknesses\n- [W1] The environments, while varied, are still relatively small in size and abstraction. It would be valuable to evaluate HypRL on more complex domains, if possible.\n- [W2] Although HypRL outperforms PPO in the wildfire scenario, the number of steps required remains large compared to the optimal policy, raising concerns about sample efficiency and scalability.\n- [W3] The technical content, especially the use of Skolemization and robustness evaluation, is quite dense and may hinder accessibility for a broader audience.\n\nQUESTIONS:\nDo the authors have any intuition or preliminary ideas on how HypRL could be extended to handle partially observable environments?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces HYPRL for learning multi-agent control policies using HyperLTL specifications. The key contributions include using Skolemization to handle quantifier alternation and quantitative semantics for reward shaping. Through experiments, the authors show HYPRL outperforms basedline on safety-aware planning and  the deep sea treasure problem.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The idea of incorporating HyperLTL for expressing complex multi-agent objectives is novel to me. As HyperLTL can capture relational properties and dependencies among agents, the proposed approach has advantage over standard LTL based approaches. \n2. The definition of quantitative semantics for HyperLTL, which translate satisfaction checking into an optimization problem, is a clever way to enable reward shaping for RL.\n3. This paper provides a thorough empirical evaluation on different benchmarks. The results demonstrate significant improvements. \n\nWeaknesses:\n1. While HyperLTL is natural for multi-agent tasks, it is also much more complex compared to other simpler logics, which could be more expensive to solve. The paper could have discussed more about the scalability of the HYPRL approach, both in terms of the number of agents and the complexity of the HyperLTL specifications, and how it compares to alternative approaches.\n2. When comparing to other baselines like PPO, the reward function is not carefully designed for your use cases. I believe one can learn/design a more powerful reward function with IRL or imitation learning.\n\nQUESTIONS:\nHow does the complexity of HYPRL scale with the size of the HyperLTL formula (e.g., number of operators, quantifier alternations) and the number of agents involved? Can you provide any theoretical bounds or empirical insights into the practical limits of the approach?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces HYPRL, a reinforcement learning framework that solves the difficult problem of designing rewards for complex multi-agent tasks described using hyperproperties. The framework allows users to define intricate objectives and dependencies between agents using the formal logic of HyperLTL which is then automatically translated into a numerical reward signal (i.e., a robustness score). This is  maximized via a centralized reinforcement learning (RL) algorithm to find coordinated policies that satisfy the original requirements.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths:\n\n- HyperLTL captures multi-agent tasks not describable easily by vanilla LTL such as quantifier logic dependent on different agents. It solves the tasks by means of Skolemization of the existential quantified agent policy which is then fed to a centralized RL algorithm.\n- The reward shaping is automatic from the specification and the approach is shown to be agnostic to the RL algorithm used with applications using PPO, DQN and CQ-Learning.\n\n## Weaknesses:\n\n- Only considers the 2-agent setting and a single universal plus existential quantifier in sequence in the experiments.\n- Assumes fully observed environments which may be hard in the presence of multiple other agents.\n- It appears that collisions are **more** than the vanilla case of CQ in the SRL environments (albeit in a shorter completion time). Given that safety is part of the specification, this is concerning.\n\nQUESTIONS:\n1. What are the scalability limits of the approach in terms of the state-space and action-space dimensions studied?\n2. How would the system prioritize safety (less collisions) without a manually constructed shield?\n3. How are max-min in the robustness semantics differentiated through? Have “soft” versions of max-min been used?\n4. What are the exact state-space or action-space augmentations used in the RL algorithm? Is there a way to decentralize execution?\n\nLIMITATIONS:\n- Only shown on a 2-agent case (scaling to n-agents may pose challenges)\n- The algorithm is centralized making it unsuitable for large agent populations.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}