The large-scale deployment of smart metering worldwide has ignited renewed interest in electrical load disaggregation, or non-intrusive load monitoring (NILM). Most NILM algorithms disaggregate one appliance at a time, remove the estimated appliance contribution from the total load, and then move on to disaggregate the next appliance. On one hand, this is efficient since multi-class classification is avoided and analytical models for each appliance can be developed independently of other appliances with the benefit of being transferred to unseen houses that have different sets of appliances. On the other hand, however, these methods can significantly under- or over- estimate the total consumption since they do not minimize the difference between the measured aggregate load and the sum of estimated individual loads. Motivated by minimizing the latter difference without losing the benefits of existing NILM algorithms, we propose novel post-processing approaches for improving the accuracy of existing NILM. This is posed as an optimization problem to refine the final NILM result using regularization based on the level of confidence in the original NILM output. We propose a heuristic method to solve this (combinatorial) Boolean quadratic problem through relaxing zero-one constraint sets to compact zero-one intervals. Convex-based solutions, including norm-1, norm-2, and semi-definite programming-based relaxation, are proposed trading off accuracy and complexity. We demonstrate good performance of the proposed post-processing methods, applicable to any event-based NILM, compared with four state-of-the-art benchmarks, using public REFIT and REDD electrical load datasets.