Online Linear Programming with Uncertain Constraints : (Invited Paper)

There are many applications scenarios in different disciplines where the critical knowledge of decision making arrives in a sequential manner, so the optimization must be done in an online fashion. An important class of online optimization problems that have been extensively studied in the past is online linear programs. This paper tackles a general class of online linear programs that take into account the online arrival of the constraint entries related to the available budget and demand for different problem settings. This generalization is motivated by many recent applications on revenue management or resource allocation problems with the unknown and time-varying budget. As the main contribution of this paper, we propose a decoupling strategy that can be used to reduce the general problem into a series of subproblems with offline entries for the budget and demand. Using the proposed strategy, one can decouple the general problem, leverage the state-of-the-art algorithms for the online subproblems with fixed constraints, and achieve the same performance for the general problem. As for a case study, we apply the strategy to an extension of the one-way trading problem with the dynamic budget.