  This paper studies the online stochastic resource allocation problem (RAP)
with chance constraints. The online RAP is a 0-1 integer linear programming
problem where the resource consumption coefficients are revealed column by
column along with the corresponding revenue coefficients. When a column is
revealed, the corresponding decision variables are determined instantaneously
without future information. Moreover, in online applications, the resource
consumption coefficients are often obtained by prediction. To model their
uncertainties, we take the chance constraints into the consideration. To the
best of our knowledge, this is the first time chance constraints are introduced
in the online RAP problem. Assuming that the uncertain variables have known
Gaussian distributions, the stochastic RAP can be transformed into a
deterministic but nonlinear problem with integer second-order cone constraints.
Next, we linearize this nonlinear problem and analyze the performance of
vanilla online primal-dual algorithm for solving the linearized stochastic RAP.
Under mild technical assumptions, the optimality gap and constraint violation
are both on the order of $\sqrt{n}$. Then, to further improve the performance
of the algorithm, several modified online primal-dual algorithms with heuristic
corrections are proposed. Finally, extensive numerical experiments on both
synthetic and real data demonstrate the applicability and effectiveness of our
methods.
