Acceleration of Evolutionary Processes by Learning and Extended Fisher's Fundamental Theorem
2021
Natural selection is general and powerful concept not only to explain
evolutionary processes of biological organisms but also to design engineering
systems such as genetic algorithms and particle filters. There is a surge of
interest, both from biology and engineering, in considering natural selection
of intellectual agents that can learn individually. Learning by individual
agents of better behaviors for survival may accelerate the evolutionary
processes by natural selection. We have accumulating pieces of evidence that
organisms can transmit its information to the next generation via epigenetic
states or memes. Also, such idea is important for engineering applications. To
accelerate the evolutionary process, an agent should change their strategy so
that the population fitness increases the most. Equivalently, an agent should
update the strategy towards a gradient of the population fitness. However, it
has not yet been clarified whether and how an agent can estimate the gradient
and accelerate the evolutionary process. We also lack methodology to quantify
the acceleration to understand and predict the impact of learning. In this
paper, we address these problems. We show that an learning agent can accelerate
the evolutionary process by proposing ancestral learning, which uses the
information transmitted from the ancestor (ancestral information). We next show
that the ancestral information is sufficient to estimate the gradient. In
particular, learning can accelerate the evolutionary process without
communications between agents. Finally, to quantify the acceleration, we extend
the Fisher's fundamental theorem (FF-thm) for natural selection to ancestral
learning. Our extended FF-thm relates the acceleration of the evolutionary
process to the variety of individual fitness of the agent. By the theorem, we
can quantitatively understand when and why learning is beneficial.
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