Mutual Learning in Optimization

In two earlier papers presented at the 2019 and 2020 American Control Conferences, the concept of “Mutual Learning” was introduced by the authors and applied to learning in static and dynamic stochastic environments. In this paper, we extend the concept of mutual learning to optimization. Two agents attempting to optimize the same performance index “learn” from each other to reach the solution more efficiently. Since optimization is a well investigated mathematical area in systems theory, it is particularly well suited to the original objective of the authors to study “Mutual Learning” in a systems theoretic framework.The two agents involved in mutual learning can use any of the methods well-known in the literature to optimize the given function. The initial conditions and the period over which the optimization is carried out, may be different for the two agents before they communicate with each other for the first time. The principal conclusion of the paper is that mutual learning should be viewed as a general research area, and not as a specific procedure used in different system theoretic problems.