Certified policy verification and synthesis for MDPs under distributional reach-avoidance properties

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 transform...

Full description

Saved in:
Bibliographic Details
Main Authors: AKSHAY, S., CHATTERJEE, Krishnendu, MEGGENDORFER, Tobias, ZIKELIC, Dorde
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2024
Subjects:
Online Access:https://ink.library.smu.edu.sg/sis_research/9340
https://ink.library.smu.edu.sg/context/sis_research/article/10340/viewcontent/0001.pdf
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Singapore Management University
Language: English
Description
Summary: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.