On a fundamental predictability-distortion trade-off in decentralized decisional networks

Decentralized decisional networks are composed of agents that take coordinated decisions on the basis of individual noisy information about the system state, i.e. under a so

called distributed state information configuration. In such scenarios, the application of algorithms directly derived from classical centralized optimization often incurs severe performance degradation. This is because the agents fail to predict each other’s decision due to local state information noise, hence they do not coordinate properly. On the other hand coordination can be easily enhanced by letting one agent reduce its dependency with respect to its state information, thus making its decision more predictable but less adapted to the system state. This observation naturally leads to formulating a fundamental trade-off, coined here predictability-distortion trade off. The goal of this paper is to formulate this trade-off and propose a framework to explore it, based on a concept of quantization under predictability constraint.