HSVI-based Online Minimax Strategies for Partially Observable Stochastic Games with Neural Perception Mechanisms
This work addresses a specific challenge in game theory for agents with asymmetric information, offering a more computationally efficient solution but is incremental in nature.
The authors tackled the problem of computing minimax strategies in continuous-state partially observable stochastic games with neural perception mechanisms, presenting an efficient online method that requires only one linear program per agent per stage and achieves ε-minimax guarantees.
We consider a variant of continuous-state partially-observable stochastic games with neural perception mechanisms and an asymmetric information structure. One agent has partial information, with the observation function implemented as a neural network, while the other agent is assumed to have full knowledge of the state. We present, for the first time, an efficient online method to compute an $\varepsilon$-minimax strategy profile, which requires only one linear program to be solved for each agent at every stage, instead of a complex estimation of opponent counterfactual values. For the partially-informed agent, we propose a continual resolving approach which uses lower bounds, pre-computed offline with heuristic search value iteration (HSVI), instead of opponent counterfactual values. This inherits the soundness of continual resolving at the cost of pre-computing the bound. For the fully-informed agent, we propose an inferred-belief strategy, where the agent maintains an inferred belief about the belief of the partially-informed agent based on (offline) upper bounds from HSVI, guaranteeing $\varepsilon$-distance to the value of the game at the initial belief known to both agents.