Current computational models have not been able to account for the effect of reward in confidence reports among humans. Here we propose a mathematical framework of confidence that is able to generalize across various decision making tasks involving varying prior and reward distributions. This framework proposes a formal definition of "decision confidence" through the concept of soft optimality. We further show that the objective function in this framework is jointly maximising the reward and information entropy of the policy. We confirm the validity of our framework by testing it on a data gathered under various task conditions.