We study how learning shapes behavior towards risk when individuals are not assumed to know, or to have beliefs about, probability distributions. In any period, the behavior change induced by learning is assumed to depend on the action chosen and the payoff obtained. We characterize learning processes that, in expected value, increase the probability of choosing the safest actions and provide sufficient conditions for them to converge to the choices of risk averse expected utility maximizers. We provide a learning theoretic motivation for long run risk choices, such as those in expected utility theory with known payoff distributions.