  We study a model of irreversible investment for a decision-maker who has the
possibility to gradually invest in a project with unknown value. In this
setting, we introduce and explore a feature of "learning-by-doing", where the
learning rate of the unknown project value is increasing in the
decision-maker's level of investment in the project. We show that, under some
conditions on the functional dependence of the learning rate on the level of
investment (the "signal-to-noise" ratio), the optimal strategy is to invest
gradually in the project so that a two-dimensional sufficient statistic
reflects below a monotone boundary. Moreover, this boundary is characterised as
the solution of a differential problem. Finally, we also formulate and solve a
discrete version of the problem, which mirrors and complements the continuous
version.
