Formal Reachability Analysis for Multi-Agent Reinforcement Learning Systems

Reachability analysis is one of the most basic and challenging problems in verification. We investigate this problem in multi-agent reinforcement learning (MARL) system by transforming the reachability analysis to decision-making problem tackled by mixed integer linear programming (MILP) solver Gurobi. We define syntax and semantics for multi-role strategy logic (mrSL) which is used to describe the reachability specification. The logic mrSL is a variant of SL to express properties, which provide a holistic perspective to describe reachability properties instead of specifying a specific agent reaches a certain state in the MARL system. And the algorithms to translate reachability property into MILP constraints are provided. A tool called MAReachAnalysis is introduced, which uses Gurobi to solve the corresponding reachability problem and evaluate it on the predator-prey task of multi-agent deep deterministic policy gradient (MADDPG) example, discussion of the experimental results obtained on a range of test cases.