Core Concepts

The authors propose a novel model called one-sided neuro-symbolic partially observable stochastic games (NS-POSGs) that explicitly incorporates neural perception mechanisms for one of the agents in a continuous-state environment. They develop a solution method called one-sided NS-HSVI that exploits the piecewise constant structure of the model and leverages neural network pre-image analysis to construct finite polyhedral representations.

Abstract

The paper introduces the model of one-sided neuro-symbolic partially observable stochastic games (NS-POSGs), which extends continuous-state concurrent stochastic games to incorporate neural perception mechanisms for one of the agents. In this model, one agent has full information about the environment, while the other agent has only partial observability and uses a data-driven neural network to perceive the continuous state space.
The authors prove that the value function of one-sided NS-POSGs is continuous and convex, and can be represented as a fixed point of a minimax operator. They then show that under mild assumptions, the value function can be represented as a piecewise linear and convex function over a polyhedral partition of the state space, which is closed under the minimax operator.
Based on this representation, the authors develop a variant of the heuristic search value iteration (HSVI) algorithm, called one-sided NS-HSVI, to approximate the value function and synthesize strategies for the agents. The algorithm uses a particle-based belief representation and exploits neural network pre-image analysis to construct the polyhedral partition efficiently.
The authors demonstrate the practical applicability of their approach on two scenarios: a pedestrian-vehicle interaction example and a pursuit-evasion game. The results show that one-sided NS-HSVI can effectively handle models with complex neural perception mechanisms and explore trade-offs in the precision of the perception function.

Stats

The reward structure r is bounded, with lower bound L = mins∈S,a∈A r(s, a)/(1-β) and upper bound U = maxs∈S,a∈A r(s, a)/(1-β), where β is the discount factor.

Quotes

"Stochastic games are a well established model for multi-agent sequential decision making under uncertainty. In practical applications, though, agents often have only partial observability of their environment. Furthermore, agents increasingly perceive their environment using data-driven approaches such as neural networks trained on continuous data."
"We propose the model of neuro-symbolic partially-observable stochastic games (NS-POSGs), a variant of continuous-space concurrent stochastic games that explicitly incorporates neural perception mechanisms."

Key Insights Distilled From

by Rui Yan,Gabr... at **arxiv.org** 04-25-2024

Deeper Inquiries

To extend the one-sided NS-HSVI algorithm to handle more than two agents in the game, we would need to adjust the belief representations and computations to accommodate the additional agents. One approach could be to introduce separate sets of particles for each agent's beliefs and update them accordingly during the algorithm's execution. The minimax strategy profiles would need to be computed for each agent, considering their interactions with the other agents in the game. The forward exploration heuristic would also need to be modified to account for the increased complexity of the multi-agent interactions. Overall, the algorithm would need to be adapted to handle the expanded state space and action sets resulting from the presence of more agents.

The piecewise linear and convex representation of the value function, while effective for certain applications, may have limitations in more complex scenarios. One potential limitation is the scalability of the representation as the state space grows larger or becomes more continuous. In such cases, the number of regions in the piecewise representation may increase significantly, leading to computational challenges. To address this limitation, the representation could be further generalized by incorporating adaptive partitioning techniques that dynamically adjust the regions based on the distribution of beliefs and observations. Additionally, exploring alternative function approximations, such as neural networks or Gaussian processes, could provide more flexibility in capturing the value function's complexity in diverse environments.

The techniques developed in the paper, such as the neuro-symbolic partially observable stochastic games (NS-POSGs) model and the heuristic search value iteration (HSV) algorithm, can be applied to a wide range of multi-agent decision-making problems beyond stochastic games. For instance, in the context of multi-agent reinforcement learning, the NS-POSG model could be utilized to represent scenarios where agents have partial observability and interact in complex environments. The HSV algorithm could be adapted to approximate optimal strategies and values in reinforcement learning settings, considering the uncertainty and partial information present in the environment. Similarly, in cooperative planning scenarios, the NS-POSG model could help model the interactions between agents with different levels of information, while the HSV algorithm could aid in synthesizing coordinated strategies for achieving common goals. By applying these techniques to diverse multi-agent decision-making problems, researchers can explore new avenues for addressing challenges in autonomous systems, robotics, and other AI applications.

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