Matteo Penlington, Lorenzo Fiaschi, Raj Kiriti Velicheti, Andrea Censi, Emilio Frazzoli
The regulation of systems composed of many interacting decentralised agents is a long-standing problem. This problem has typically been resolved by the imposition of rules. Rules resolve the limitations of sub-optimal agents whilst simultaneously aligning the behaviour of the agents with the demands of society. Traffic laws, for example, let a driver cross a junction without seeing around the corner, and transport protocols such as TCP let applications share a network without knowing of one another. The problem is more pressing today, as autonomous systems are deployed in society. In this work, we establish the basis of a system-agnostic theory of rule design for multi-agent systems. We first state the rule design problem (RDP) in its generality. It relates a rule to the set of system performances, defined by the regulator, that the agents deployed under it can attain. However, it is not yet possible to solve the RDP in full generality. As such, we introduce the homogeneous rule design problem (HRDP), in which the agents in each environment are identical, and among other interesting properties, show that under worst-case aggregation the two problems have the same solution, bypassing the combinatorial complexity of the RDP. To solve the RDP under worst-case aggregation we propose Rule Branch and Bound (RuleBnB), an anytime branch-and-bound algorithm. Finally, we illustrate the value of solving the RDP on an autonomous driving case study.
Yueshan Li, Lorenzo Fiaschi, Andrea Censi, Emilio Frazzoli
Independently developed autonomous agents, such as autonomous vehicles, must guarantee joint compatibility, such as safety and task-completion requirements, when they operate in a shared environment. Existing methods require a centrally designed specification, or interaction mechanism before any agent is deployed. However, such centralized design is unrealistic when agent designs are confidential to their developers, and it is not flexible enough to accommodate future agent designs. We study a bi-level structure in which a regulator coordinates developers by publishing seed agents, and each developer independently tests its agent to ensure that it is compatible with every seed-compatible agent, a property we call future-proofness. Under this structure, joint compatibility is guaranteed for any agents that are designed and tested independently, without any coordination with each other. In this work, we first formulate compatibility for general multi-agent systems and show why it is not trivially implied by seed-compatibility. We then characterize the future-proof agents as the closure of the seed and show that this closure is monotone in the seed. Finally, we study a class of executable tests that involve interaction with the seed alone, and we ask to what extent such tests can distinguish the future-proof agents.