local maximum

A local maximum for a function is a set of parameters for the function that is the largest in a neighbourhood, that is f(p) > f(p+δ) for small changes $delta; in the parametre value. In a physical landscape this would correspond to the top of a small hill, but where there may be a much larger hill elsewhere. This geographic analogy can be helpful in the case of the firness landcape egnerated by a fitness function for machine learning; however, whlst the space of parametres for a physicla lcation is 2D (latitued,longitude), the space of parameters of a ftness functoon is often multi-dimensional and may include a mix of different kinds of parameters, not just numeric. It is the opposite of a local minimum and is to be contrasted with a global maximum which is the largest/highest point overall.