This paper addresses a novel optimal supervisory control problem for reachability tasks in partially-known discrete-event systems (DES). We consider a setting where the supervisor lacks prior knowledge of feasible events in certain states and must discover this information by visiting them. To assess performance in this context, we study regret as a metric that quantifies the difference between the actual cost incurred and the optimal cost achievable with full knowledge. We formalize this problem and propose the algorithm to compute an optimal supervisor that guarantees reachability while minimizing regret. Our results demonstrate that regret serves as a meaningful performance measure for supervisory control in partially-known DES, and our method is both correct and effective in practice.