Strategy Synthesis for ZeroSum NeuroSymbolic Concurrent Stochastic Games
Abstract
Neurosymbolic approaches to artificial intelligence, which combine neural networks with classical symbolic techniques, are growing in prominence, necessitating formal approaches to reason about their correctness. We propose a novel modelling formalism called neurosymbolic concurrent stochastic games (NSCSGs), which comprise probabilistic finitestate agents interacting in a shared continuousstate environment observed through perception mechanisms implemented as neural networks (NNs). We focus on the class of NSCSGs with Borel state spaces and prove the existence and measurability of the value function for zerosum discounted cumulative rewards under piecewiseconstant restrictions on the components of this class of models. To compute values and synthesise strategies, we present, for the first time, implementable value iteration (VI) and policy iteration (PI) algorithms to solve a class of continuousstate CSGs. These require a finite representation of the preimage of the environment's NN perception mechanism and rely on finite abstract representations of value functions and strategies closed under VI or PI. First, we introduce a Borel measurable piecewiseconstant (BPWC) representation of value functions, extend minimax backups to this representation and propose BPWC VI. Second, we introduce two novel representations for the value functions and strategies, constantpiecewiselinear (CONPWL) and constantpiecewiseconstant (CONPWC) respectively, and propose Minimaxactionfree PI by extending a recent PI method based on alternating player choices for finite state spaces to Borel state spaces, which does not require normalform games to be solved. We illustrate our approach with a dynamic vehicle parking example by generating approximately optimal strategies using a prototype implementation of the BPWC VI algorithm.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 DOI:
 10.48550/arXiv.2202.06255
 arXiv:
 arXiv:2202.06255
 Bibcode:
 2022arXiv220206255Y
 Keywords:

 Computer Science  Artificial Intelligence;
 Computer Science  Computer Science and Game Theory;
 Computer Science  Logic in Computer Science
 EPrint:
 50 pages, 5 figures