In general, an equilibrium will inform machine learning by seeking to stabilize machine learning environments and create outcomes with a compatible mix of deterministic and probabilistic components.
Experts describe an "equilibrium" as a situation where rational actors in a machine learning system reach a consensus on strategic action – in particular, the Nash equilibrium in game theory involves two or more of these rational actors consolidating strategies by recognizing that no player benefits by changing a particular strategy if the other players do not change theirs.
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A particularly popular and simple demonstration of Nash equilibrium involves a simple matrix where two players each choose a binary outcome.
The above is a pretty technical way to describe equilibrium and how it works. A much more informal way to illustrate the concept of equilibrium, particularly the above example of two rational actors each having binary choice, is to think about what you might call the "walking toward each other in the high school hallway" scenario.
Suppose two people walk in different directions down a high school hallway (or any other type of area), that only has room for two people width-wise. The two open paths are the binary outcomes. If the two rational actors choose different binary outcomes that don’t conflict with each other, they will pass by each other and say hello. If they choose two conflicting binary outcomes – they’re walking in the same space, and one of them will need to yield.
In the above example, if the two rational actors choose the two compatible and non-conflicting outcomes, the general consensus is that neither one gains by changing their strategy – in this case their walking directions – if the other person does not change theirs.
The above constitutes an equilibrium that can be modeled in any given machine learning construct. Given this simple example, the outcome will always be the two rational actors cooperating, or in other words, two people walking past each other.
The opposite could be called a "disequilibrium" – if the two rational actors choose conflicting outcomes, as mentioned, one of them will have to yield. However, the ML program modeling this could be thrown into an infinite loop if both decide to yield – much like two people to move to try to accommodate each other and still continue to walk toward collision.
Equilibriums like the one above one will generally be used in machine learning to create consensus and stabilize models. Engineers and developers will look for those scenarios and situations that benefit from equilibriums, and work to change or handle those that don't. Looking at real-world examples that correspond to ML equilibriums, it’s easy to see how this kind of analysis in machine learning system is uniquely instructive for figuring out how to model human behavior by creating rational actors and agents. That's just one excellent example of how an equilibrium can be used to make advances in the application of machine learning systems.