Finite-horizon Equilibria for Neuro-symbolic Concurrent Stochastic Games

TL;DR

This paper introduces new methods for finding equilibria in neuro-symbolic concurrent stochastic games, enabling agents with different goals to operate effectively in continuous environments.

Contribution

It formalizes equilibrium concepts for neuro-symbolic stochastic games and proposes an approximation algorithm, addressing limitations of previous zero-sum models.

Findings

The proposed algorithm improves equilibrium quality over backward induction methods.

Application to case studies demonstrates practical effectiveness.

Approximate solutions are computationally feasible for complex scenarios.

Abstract

We present novel techniques for neuro-symbolic concurrent stochastic games, a recently proposed modelling formalism to represent a set of probabilistic agents operating in a continuous-space environment using a combination of neural network based perception mechanisms and traditional symbolic methods. To date, only zero-sum variants of the model were studied, which is too restrictive when agents have distinct objectives. We formalise notions of equilibria for these models and present algorithms to synthesise them. Focusing on the finite-horizon setting, and (global) social welfare subgame-perfect optimality, we consider two distinct types: Nash equilibria and correlated equilibria. We first show that an exact solution based on backward induction may yield arbitrarily bad equilibria. We then propose an approximation algorithm called frozen subgame improvement, which proceeds through iterative solution of nonlinear programs. We develop a prototype implementation and demonstrate the benefits of our approach on two case studies: an automated car-parking system and an aircraft collision avoidance system.