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This paper studies the online stochastic resource allocation problem (RAP)with chance constraints. The online RAP is a 0-1 integer linear programmingproblem where the resource consumption coefficients are revealed column bycolumn along with the corresponding revenue coefficients. When a column isrevealed, the corresponding decision variables are determined instantaneouslywithout future information. Moreover, in online applications, the resourceconsumption coefficients are often obtained by prediction. To model theiruncertainties, we take the chance constraints into the consideration. To thebest of our knowledge, this is the first time chance constraints are introducedin the online RAP problem. Assuming that the uncertain variables have knownGaussian distributions, the stochastic RAP can be transformed into adeterministic but nonlinear problem with integer second-order cone constraints.Next, we linearize this nonlinear problem and analyze the performance ofvanilla online primal-dual algorithm for solving the linearized stochastic RAP.Under mild technical assumptions, the optimality gap and constraint violationare both on the order of $\sqrt{n}$. Then, to further improve the performanceof the algorithm, several modified online primal-dual algorithms with heuristiccorrections are proposed. Finally, extensive numerical experiments on bothsynthetic and real data demonstrate the applicability and effectiveness of ourmethods.

An Online Algorithm for Chance Constrained Resource Allocation