There is self religion:
A self religion (or self-religion) is a religious or self-improvement group which has as one of its primary aims the improvement of the self
Also stoicism has self-help (self-improvement) ideology in it.
The Stoics taught that destructive emotions resulted from errors in judgment, and that a sage, or person of "moral and intellectual perfection," would not suffer such emotions.
Philosophy for a Stoic is not just a set of beliefs or ethical claims, it is a way of life involving constant practice and training (or askesis, see asceticism)
A word for a person or concept that puts emphasis on self-improvement would be "flourishing".
In positive psychology, flourishing is “to live within an optimal range of human functioning, one that connotes goodness, generativity, growth, and resilience.”
Thus, eudaimonia or eudaimonism is a related concept. It is a Greek word but it is also a loan word in English. In modern psychology, it is conceptualized in six factors, one of which is personal growth.
Eudaimonia, sometimes anglicized as eudaemonia or eudemonia , is a Greek word commonly translated as happiness or welfare; however, "human flourishing" has been proposed as a more accurate translation.
Etymologically, it consists of the words "eu" ("good") and "daimōn" ("spirit"). It is a central concept in Aristotelian ethics and political philosophy, along with the terms "aretē", most often translated as "virtue" or "excellence", and "phronesis", often translated as "practical or ethical wisdom".
Best Answer
There's a word that has been borrowed from Japanese to describe continuous process improvement in manufacturing, "kaizen". I'm posting this as an answer based on the suggestion in the comments, and the fact that it is in several of the English dictionaries that I checked.
Ngram: kaizen.
(from dictionary.reference.com)