# Certified Policy Verification and Synthesis for MDPs under Distributional Reach-avoidance Properties

arXiv: https://arxiv.org/abs/2405.04015 · HTML: https://mlsanity.com/paper/2405.04015/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 7 May 2024.

## Builds on (most cited first, 14 of 14)

- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Stability Verification in Stochastic Control Systems via Neural Network Supermartingales](https://mlsanity.com/paper/2112.09495/) (2021)
- [Learning Control Policies for Stochastic Systems with Reach-avoid Guarantees](https://mlsanity.com/paper/2210.05308/) (2022)
- [Compositional Policy Learning in Stochastic Control Systems with Formal Guarantees](https://mlsanity.com/paper/2312.01456/) (2023)
- [StocHy: automated verification and synthesis of stochastic processes](https://mlsanity.com/paper/1901.10287/) (2019)
- [Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise](https://mlsanity.com/paper/2110.12662/) (2021)
- [FAUST2: Formal Abstractions of Uncountable-STate STochastic processes](https://mlsanity.com/paper/1403.3286/) (2014)
- [Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making](https://mlsanity.com/paper/1504.06002/) (2015)
- [Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty](https://mlsanity.com/paper/2210.05989/) (2022)
- [AMYTISS: Parallelized Automated Controller Synthesis for Large-Scale Stochastic Systems](https://mlsanity.com/paper/2005.06191/) (2020)
- [MDPs as Distribution Transformers: Affine Invariant Synthesis for Safety Objectives](https://mlsanity.com/paper/2305.16796/) (2023)
- [Limit Synchronization in Markov Decision Processes](https://mlsanity.com/paper/1310.2935/) (2013)
- [Distribution-based objectives for Markov Decision Processes](https://mlsanity.com/paper/1804.09341/) (2018)
- [Anytime Guarantees for Reachability in Uncountable Markov Decision Processes](https://mlsanity.com/paper/2008.04824/) (2020)

## Built on by (most cited first, 2 of 2)

- [Entropy Objectives in Markov Decision Processes](https://mlsanity.com/paper/2606.21726/) (2026)
- [Certifying Almost-Sure Reachability in Unknown MDPs](https://mlsanity.com/paper/2610.18119/) (2026)

## Abstract (arXiv)

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.