Investigating machine learning decision problems with game theory.

摘要

The machine learning domain has many decision problems that must by considered when using the various techniques found within it. A decision problem occurs when a "yes" or "no" answer to a question depends on the current input configuration of a system or the environment in which that question is relevant. Our focus is unsupervised machine learning, where learning rules are executed automatically without the intervention of a user after an initial data cleansing stage. This is an automated process with the modification of variables being automatic through the use of robust algorithms. It arises in some situations, however, that a decision problem must be solved in order to direct the algorithm along a correct path. Failure to do this results in the algorithm giving a less-than-ideal result. Game theory, it is discovered in this dissertation, is an excellent resource for determining the correct path to follow. It allows us to accurately describe the decision problem in terms of observed evidence.;In this dissertation, we describe two machine learning sub-domains in which game;theory is useful in solving some decision problems found within them. The first domain, neural networks, benefits from game theory in the competitive learning model. The game-theoretic self-organizing map model (a special type of neural network) is reviewed and extended to a growing hierarchical model to increase its robustness. We introduce Outward Update Propagation as a method of ensuring pattern consistency within the hierarchical maps.;The second domain, rough sets, benefits from game theory in respect to data-driven probabilistic thresholds. The game-theoretic rough set model is introduced as an example of game-theoretic machine learning. We make the connection that the parameter optimization decision problem is highly similar to that of a competitive game. Since reducing the size of the boundary region is our goal, we can formulate two types of games with this model: strict competition between regions or the formation of a coalition to achieve a level of balance between the two regions. These two areas of study show the effectiveness of game theory to analyze a variety of decision problems faced by researchers.;Game theory is a powerful method for mathematically formulating decision problems as competition between two or more entities. To formulate a decision problem in game theory, one requires information regarding the players in the game (those with a position to directly influence the decision), the actions that can be performed to influence a decision, and the resulting payoff that is achieved signifying that a decision is nearer to being made.