This form of learning curve is used extensively in industry for cost projections * S-Curve or Sigmoid function In this case the improvement of proficiency starts slowly, then increases rapidly, and finally levels off. (Fig 7) The page on “Experience curve effects” offers more discussion f the mathematical theory of representing them as deterministic processes, and provides a good group of empirical examples of how that technique has been applied. – [edit]Learning curve in machine learning 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. The machine learning curve is useful for many purposes including comparing different algorithms, choosing model parameters during design adjusting optimization to improve convergence, and determining the amount of data used for training.[edit]Broader interpretations of the learning curve 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. In economics the subject is rates of “development”, as development refers to a whole yester learning process with varying rates of progression.
Generally speaking all learning displays incremental change over time, but describes an “S” curve which has different appearances depending on the time scale of observation. It has now also become associated with the evolutionary theory of punctuated equilibrium and other kinds of revolutionary change in complex systems generally, relating connotation, organizational behavior and the management of group learning, among other fields. 24] These processes of rapidly emerging new form appear to take place y complex learning within the systems themselves, which when observable, display curves of changing rates that accelerate and decelerate. [edit]General learning limits 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. 25] These practical experiences match the predictions of the second law of thermodynamics for the limits of waste reduction nearly. Approaching limits of perfecting things to eliminate waste meets geometrically increasing effort to make progress, and provides an environmental measure of all factors seen and unseen changing the learning experience. Perfecting things becomes ever more difficult despite increasing effort despite continuing positive, if ever diminishing, results.
The same kind of slowing progress due to complications in learning also appears in the limits of useful technologies and of profitable markets applying to product life cycle management and software development cycles). Remaining market segments or remaining potential efficiencies or efficiencies are found in successively less convenient forms. 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. * Natural Limits One of the key studies in the area concerns diminishing returns on investments generally, either physical or uncial, pointing to whole system limits for resource development or other efforts. The most studied of these may be Energy Return on Energy Invested or ERROR, discussed at length in an Encyclopedia of the Earth article and in an Older article and series also referred to as Hubert curves.
The energy needed to produce energy is a measure of our difficulty in learning how to make remaining energy resources useful in relation to the effort expended. Energy returns on energy invested have been in continual decline for some time, caused by natural resource limits and increasing investment. Energy is both nature’s and our own principal resource for making things happen. The point of diminishing returns is when increasing investment makes the resource more expensive.
As natural limits are approached, easily used sources are exhausted and ones with more complications need to be used instead. As an environmental signal persistently diminishing ERROR indicates an approach of whole system limits in our ability to make things happen. * Useful Natural Limits ERROR measures the return on invested effort as a ratio of RI or learning progress. The inverse AIR measures learning difficulty. The simple difference is that if R approaches zero RI will too, but AIR will approach infinity.
When complications emerge to limit learning progress the limit of useful returns, our, is approached and R-our approaches zero. The difficulty of useful learning/(R-our) approaches infinity as increasingly difficult tasks make the effort unproductive. That point is approached as a vertical asymptote, at a particular point in time, that can be delayed only by unsustainable effort. It defines a point at which enough investment has been made and the task is done, usually planned to be the same as when he task is complete. For unplanned tasks it may be either foreseen or discovered by surprise.
