Online optimization is a field of optimization theory, more popular in computer science and operations research, that deals with optimization problems having no or incomplete knowledge of the future (online). These kind of problems are denoted as online problems and are seen as opposed to the classical optimization problems where complete information is assumed (offline). The research on online optimization can be distinguished into online problems where multiple decisions are made sequentially based on a piece-by-piece input and those where a decision is made only once. A famous online problem where a decision is made only once is the Ski rental problem. In general, the output of an online algorithm is compared to the solution of a corresponding offline algorithm which is necessarily always optimal and knows the entire input in advance (competitive analysis).
In many situations, present decisions (for example, resources allocation) must be made with incomplete knowledge of the future or distributional assumptions on the future are not reliable. In such cases, online optimization[1] can be used, which is different from other approaches such as robust optimization, stochastic optimization and Markov decision processes.
^Jaillet, Patrick, and Michael R. Wagner. Online Optimization. Springer Publishing Company, Incorporated, 2012.
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