# Counterexample-Guided Strategy Improvement for POMDPs Using Recurrent Neural Networks

## TL;DR

This paper introduces a novel approach combining machine learning and formal verification to synthesize strategies for POMDPs, using RNNs to encode strategies and iterative training for improvement, significantly enhancing efficiency.

## Contribution

The paper presents a new method that uses RNNs for strategy encoding in POMDPs and an iterative counterexample-guided training process, advancing the state of the art.

## Key findings

- Achieves up to three orders of magnitude faster solving times.
- Effectively encodes strategies without full belief space expansion.
- Provides provable guarantees and diagnostic counterexamples.

## Abstract

We study strategy synthesis for partially observable Markov decision processes (POMDPs). The particular problem is to determine strategies that provably adhere to (probabilistic) temporal logic constraints. This problem is computationally intractable and theoretically hard. We propose a novel method that combines techniques from machine learning and formal verification. First, we train a recurrent neural network (RNN) to encode POMDP strategies. The RNN accounts for memory-based decisions without the need to expand the full belief space of a POMDP. Secondly, we restrict the RNN-based strategy to represent a finite-memory strategy and implement it on a specific POMDP. For the resulting finite Markov chain, efficient formal verification techniques provide provable guarantees against temporal logic specifications. If the specification is not satisfied, counterexamples supply diagnostic information. We use this information to improve the strategy by iteratively training the RNN. Numerical experiments show that the proposed method elevates the state of the art in POMDP solving by up to three orders of magnitude in terms of solving times and model sizes.