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The term learning curve is used in two main ways: where the same task is repeated in a series of trials, or where a body of knowledge is learned over time. The first person to describe the learning curve was Hermann Ebbinghaus in 1885, in the field of the psychology of learning, although the name wasn’t used until 1909. The familiar expression “a steep learning curve” is intended to mean that the activity is difficult to learn, although a learning curve with a steep start actually represents rapid progress. The first person to describe the learning curve was Hermann Ebbinghaus in 1885. His tests involved memorizing series of nonsense syllables, and recording the success over a number of trials. The translation does not use the term learning curve—but he presents diagrams of learning against trial number.
Psychologist Arthur Bills gave a more detailed description of learning curves in 1934. He also discussed the properties of different types of learning curves, such as negative acceleration, positive acceleration, plateaus, and ogive curves. In 1936, Theodore Paul Wright described the effect of learning on production costs in the aircraft industry and proposed a mathematical model of the learning curve. Unit Cost model pioneered by Wright, and specifically used a Power Law, which is sometimes called Henderson’s Law. He named this particular version the experience curve. The economic learning of productivity and efficiency generally follows the same kinds of experience curves and have interesting secondary effects.
Efficiency and productivity improvement can be considered as whole organization or industry or economy learning processes, as well as for individuals. The Vertical Axis is a measure representing learning or proficiency or other proxy for “efficiency” or “productivity”. For the performance of one person in a series of trials the curve can be erratic, with proficiency increasing, decreasing or leveling out in a plateau. When the results of a large number of individual trials are averaged then a smooth curve results, which can often be described with a mathematical function. The S-Curve or Sigmoid function is the idealized general form of all learning curves, with slowly accumulating small steps at first followed by larger steps and then successively smaller ones later, as the learning activity reaches its limit. That idealizes the normal progression from discovery of something to learn about followed to the limit of what learning about it.
In this case the improvement of proficiency starts slowly, then increases rapidly, and finally levels off. This is similar in appearance to an Exponential decay function, and is almost always used for a decreasing performance metric, such as cost. It also has the property that if you plot the logarithm of proficiency against the logarithm of experience the result is a straight line, and it is often presented that way. The specific case of a plot of Unit Cost versus Total Production with a Power Law was named the Experience Curve: the mathematical function is sometimes called Henderson’s Law. This form of learning curve is used extensively in industry for cost projections. The page on “Experience curve effects” offers more discussion of the mathematical theory of representing them as deterministic processes, and provides a good group of empirical examples of how that technique has been applied.
Plots relating performance to experience are widely used in machine learning. Performance is the error rate or accuracy of the learning system, while experience may be the number of training examples used for learning or the number of iterations used in optimizing the system model parameters. Initially introduced in educational and behavioral psychology, the term has acquired a broader interpretation over time, and expressions such as “experience curve”, “improvement curve”, “cost improvement curve”, “progress curve”, “progress function”, “startup curve”, and “efficiency curve” are often used interchangeably. Learning curves, also called experience curves, relate to the much broader subject of natural limits for resources and technologies in general. Such limits generally present themselves as increasing complications that slow the learning of how to do things more efficiently, like the well-known limits of perfecting any process or product or to perfecting measurements. Efficiency and development curves typically follow a two-phase process of first bigger steps corresponding to finding things easier, followed by smaller steps of finding things more difficult. It reflects bursts of learning following breakthroughs that make learning easier followed by meeting constraints that make learning ever harder, perhaps toward a point of cessation.