TY - GEN
T1 - Certified Policy Verification and Synthesis for MDPs under Distributional Reach-avoidance Properties
AU - Akshay, S.
AU - Chatterjee, Krishnendu
AU - Meggendorfer, Tobias
AU - Žikelić, Ðorđe
N1 - Publisher Copyright:
© 2024 International Joint Conferences on Artificial Intelligence. All rights reserved.
PY - 2024
Y1 - 2024
N2 - Markov Decision Processes (MDPs) are a classical model for decision making in the presence of uncertainty. Often they are viewed as state transformers with planning objectives defined with respect to paths over MDP states. An increasingly popular alternative is to view them as distribution transformers, giving rise to a sequence of probability distributions over MDP states. For instance, reachability and safety properties in modeling robot swarms or chemical reaction networks are naturally defined in terms of probability distributions over states. Verifying such distributional properties is known to be hard and often beyond the reach of classical state-based verification techniques. In this work, we consider the problems of certified policy (i.e. controller) verification and synthesis in MDPs under distributional reach-avoidance specifications. By certified we mean that, along with a policy, we also aim to synthesize a (checkable) certificate ensuring that the MDP indeed satisfies the property. Thus, given the target set of distributions and an unsafe set of distributions over MDP states, our goal is to either synthesize a certificate for a given policy or synthesize a policy along with a certificate, proving that the target distribution can be reached while avoiding unsafe distributions. To solve this problem, we introduce the novel notion of distributional reach-avoid certificates and present automated procedures for (1) synthesizing a certificate for a given policy, and (2) synthesizing a policy together with the certificate, both providing formal guarantees on certificate correctness. Our experimental evaluation demonstrates the ability of our method to solve several non-trivial examples, including a multi-agent robot-swarm model, to synthesize certified policies and to certify existing policies.
AB - Markov Decision Processes (MDPs) are a classical model for decision making in the presence of uncertainty. Often they are viewed as state transformers with planning objectives defined with respect to paths over MDP states. An increasingly popular alternative is to view them as distribution transformers, giving rise to a sequence of probability distributions over MDP states. For instance, reachability and safety properties in modeling robot swarms or chemical reaction networks are naturally defined in terms of probability distributions over states. Verifying such distributional properties is known to be hard and often beyond the reach of classical state-based verification techniques. In this work, we consider the problems of certified policy (i.e. controller) verification and synthesis in MDPs under distributional reach-avoidance specifications. By certified we mean that, along with a policy, we also aim to synthesize a (checkable) certificate ensuring that the MDP indeed satisfies the property. Thus, given the target set of distributions and an unsafe set of distributions over MDP states, our goal is to either synthesize a certificate for a given policy or synthesize a policy along with a certificate, proving that the target distribution can be reached while avoiding unsafe distributions. To solve this problem, we introduce the novel notion of distributional reach-avoid certificates and present automated procedures for (1) synthesizing a certificate for a given policy, and (2) synthesizing a policy together with the certificate, both providing formal guarantees on certificate correctness. Our experimental evaluation demonstrates the ability of our method to solve several non-trivial examples, including a multi-agent robot-swarm model, to synthesize certified policies and to certify existing policies.
UR - http://www.scopus.com/inward/record.url?scp=85204313002&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85204313002
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 3
EP - 12
BT - Proceedings of the 33rd International Joint Conference on Artificial Intelligence, IJCAI 2024
A2 - Larson, Kate
PB - International Joint Conferences on Artificial Intelligence
T2 - 33rd International Joint Conference on Artificial Intelligence, IJCAI 2024
Y2 - 3 August 2024 through 9 August 2024
ER -