I. Introduction
Many scenarios in smart infrastructure systems require a system operator to incentivize self-interested agents to exert costly effort to make decisions that align with the goal of the operator. For instance, in participatory sensing, a system operator requires many autonomous sensors to take measurements to allow estimation of a global quantity. The operator cannot observe directly the effort of each sensing agent (possibly for privacy reasons) and the agent might not benefit directly from the goal of the operator and thus needs to be compensated based on noisy outputs. Incentive design in this setting has been analyzed, particularly in the context of participatory sensing and crowd sensing, for classical estimation as well as learning based tasks (see [1], [2] and the references therein).