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.
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