Mathematical Description
Hill climbing attempts to maximize (or minimize) a target function, where is a vector of continuous and/or discrete values. At each iteration, hill climbing will adjust a single element in and determine whether the change improves the value of . (Note that this differs from gradient descent methods, which adjust all of the values in at each iteration according to the gradient of the hill.) With hill climbing, any change that improves is accepted, and the process continues until no change can be found to improve the value of . is then said to be "locally optimal".
In discrete vector spaces, each possible value for may be visualized as a vertex in a graph. Hill climbing will follow the graph from vertex to vertex, always locally increasing (or decreasing) the value of, until a local maximum (or local minimum) is reached.
Read more about this topic: Hill Climbing
Famous quotes containing the words mathematical and/or description:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“Whose are the truly labored sentences? From the weak and flimsy periods of the politician and literary man, we are glad to turn even to the description of work, the simple record of the month’s labor in the farmer’s almanac, to restore our tone and spirits.”
—Henry David Thoreau (1817–1862)