We study belief dynamics of an agent who repeatedly ‘‘chooses’’ new beliefs, optimally trading off costs from making worse decisions with benefits from anticipatory utility. To explain non-Bayesian updating, we assume that the agent naively thinks that each choice of beliefs is the first (and last) such choice. We identify a novel ‘‘optimism-confidence’’ trade-off: the more uncertain the agent chooses to be, the more optimistic she can be, because predicted learning dampens overoptimism. In the long run this trade-off leads to persistent insecurity and fragile optimism in important domains of life and dogmatic optimism in less important domains.