Online optimisation methods try to answer a simple question: what happens to the performance of an optimsiation algorithm when the problem itself changes faster than the time required for the algorithm to return a "sensible" outcome? To this end, the notion of regret is introduced that tries to compute the loss of performance of an algorithm compared with an omniscient oracle that knows the solution to the problem. In this project, we try to address a related question: do all the possible solutions obtained from applying an algorithm in an online optimsiation setting return "comparable" solutions? This problem can be studied from the perspective of Incremental Input to State Stability.