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On Two Mechanisms Associated To Learning: A Mathematical Point Of View

We study two important features of the mechanisms living organisms seem to use to solve recurrent problems when able to choose strategies from a known set. The first one is forgetting and its influence on the ability of the organism to learn the chance of success of the known strategies. The other feature is selection of strategies according to their relative strengths. Specifically, we compare exponential and hyperbolic forgetting models, and we prove that when the agent has only one strategy available, the estimates for the strategy success rate using the exponential model never converge (in probabilistic terms), whereas the ones using the hyperbolic model converge almost surely. When more strategies are available and proportional selection is used, we prove several results that generalize the one strategy case.