Active adaptive management balances the requirements of management with the need to learn about the system being managed, which leads to better decisions. It is difficult to judge the benefit of management actions that accelerate information gain, relative to the benefit of making the best management decision given what is known at the time. We present a first step in developing methods to optimize management decisions that incorporate both uncertainty and learning via adaptive management We assumed a manager can allocate effort to discrete units (e.g., areas for revegetation or animals for reintroduction), the outcome can be measured as success or failure (e.g., the revegetation in an area is successful or the animal survives and breeds), and the manager has two possible management options from which to choose. We further assumed that there is an annual budget that may be allocated to one or both of the two options and that the manager must decide on the allocation. We used Bayesian updating of the probability of success of the two options and stochastic dynamic programming to determine the optimal strategy over a specified number of years, The costs, level of certainty about the success of the two options, and the timeframe of management all influenced the optimal allocation of the annual budget. In addition, the choice of management objective had a large influence on the optimal decision. In a case study of Merri Creek, Melbourne, Australia, we applied the approach to determining revegetation strategies. Our approach can be used to determine how best to manage ecological systems in the face of uncertainty.