Artificial intelligence (AI) systems often interact with multiple agents. The regulation of such AI systems often requires that {\em a priori\/} guarantees of fairness and robustness be satisfied. With stochastic models of agents' responses to the outputs of AI systems, such {\em a priori\/} guarantees require non-trivial reasoning about the corresponding stochastic systems. Here, we present an open-source PyTorch-based toolkit for the use of stochastic control techniques in modelling interconnections of AI systems and properties of their repeated uses. It models robustness and fairness desiderata in a closed-loop fashion, and provides {\em a priori\/} guarantees for these interconnections. The PyTorch-based toolkit removes much of the complexity associated with the provision of fairness guarantees for closed-loop models of multi-agent systems.

There has been considerable interest in the regulation of artificial intelligence (AI), recently. It is increasingly recognized that so-called high-risk applications of AI, such as in Human Resources, Retail Banking, or within public schools, be it admissions or assessment, cannot be served by black-box AI systems with no human control. It is not clear [10], however, how to phrase even the desiderata for the regulation of AI. Here, we suggest that the desiderata could be the same as in the Civil Rights Act of 1964 and much of the subsequent civil-right legislation world-wide: equal treatment and equal impact. At the same time, we point out that these desiderata could be in conflict [34]. Let us illustrate the conflict on an example of a system that performs credit-risk estimate in a consumer-credit company.