Neuro-symbolic 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 neuro-symbolic concurrent stochastic games (NS-CSGs), which comprise a set of probabilistic finite-state agents interacting in a shared continuous-state environment, observed through perception mechanisms implemented as neural networks. Since the environment state space is continuous, we focus on the class of NS-CSGs with Borel state spaces and Borel measurability restrictions on the components of the model. We consider the problem of zero-sum discounted cumulative reward, proving that NS-CSGs are determined and therefore have a value which corresponds to a unique fixed point. From an algorithmic perspective, existing methods to compute values and optimal strategies for CSGs focus on finite state spaces. We present, for the first time, value iteration and policy iteration algorithms to solve a class of uncountable state space CSGs, and prove their convergence. Our approach works by formulating piecewise linear or constant representations of the value functions and strategies of NS-CSGs. We validate the approach with a prototype implementation applied to a dynamic vehicle parking example.
翻译:将神经网络与古典象征性技术相结合的人工智能神经 -- -- 共振性理论方法日益突出,需要正式解释其正确性。我们建议采用新型的模型形式主义,称为神经-共振同时随机游戏(NS-CSGs),由一组在共同连续状态环境中互动的概率性有限物剂组成,通过作为神经网络实施的感知机制加以观察。由于环境状态空间是持续的,我们侧重于NS-CSG与波雷尔州空间的等级和对模型组成部分的可衡量性限制。我们考虑了零和折扣累积奖励的问题,证明NS-CSGs已经确定,因此具有与一个独特的固定点相匹配的价值。从算法的角度看,现有的计算CSGs价值和最佳战略的计算方法侧重于有限的状态空间。我们第一次提出,重视这种分类和政策推算算法,以解决一组不可计价的国家空间CSGs,并证明它们的一致性。我们的方法是通过制定固定的直线式或固定的车辆定位模型来实施SNSSG。