In the classical principal-agent model, the principal delegates a task to an agent who takes an action that is unobservable to the principal and that is costly. We examine this issue within a Bayesian framework where the agent’s privacy type, representing the unit cost of effort, is single-dimensional and follows a publicly known probability distribution. Each action necessitates distinct levels of effort. This conception of effort and cost per unit underpins the model’s objective to assess the approximation guarantee of linear contracts compared to optimal contracts within a Bayesian framework. Linear contracts encompass allocation rules mapping types to actions and payment rules associating types with random outcomes for a selected set of actions. We approach this problem through a computational lens. Our primary focus lies on cases where the agent determines an action set to fulfill a complex task delegated by the principal, with success being uncertain. We demonstrate that if the probability of success behaves as a submodular function of the action set, linear contracts approximate optimality under sufficient uncertainty in the principal-agent relationship.