The research of online algorithms is research of optimisation methods in dynamic limited-information settings, in constrast to traditional optimisation where the whole input is known with full certainty. Central tasks are algorithm design and analysis, as well as model definition. Many online algorithms are based on developing relatively simple heuristics to combinatorial optimisation problems and then rigorously proving their effectiveness. Some involve heavier tools such as primal-dual linear programming techniques.

For example, the traveling salesperson problem is a classic example of traditional (offline) combinatorial optimisation. A salesperson plans to visit a number of cities and seeks to identify the cheapest possible route. The travel costs (say, ticket prices) between each pair of cities are known to her. An online version of the same problem could include unknown ticket price variations during the trip, or changes in the list of cities needed to visit. It is essential that some decisions (where to travel first) must be permanently chosen before having access to a part of the optimisation information (ticket prices on the last day). The information is revealed only gradually.

Optimisation models, where the unknown information comes in form of an externally given probability distribution, fall in general in the field of stochastic optimisation. To point out the core difference, online optimisation does not assume information on probabilities. Instead the goal is to perform acceptably well in any possible instance within the used model. The typical yardstick for successfulness of online algorithms is the competitive ratio, which is the worst-case ratio between an algorithm's solution cost and the very optimal solution cost. (This is for cost minimisation settings; for profit maximisation settings one often uses the inverse of the corresponding ratio.) It is worth noting that in this comparison the optimal solution is unfairly granted with full information on the setting, and even then it might be computationally infeasible to find explicitly.

This ambiguous attitude to unforeseen parameter values leads online algorithms to some performance losses in shifting focus from typical to worst-case instances, but at the practical benefit of not needing to define 'typical' inputs or estimate and update probabilities for input parameters.