Learning to Regularized Resource Allocation with Budget Constraints

Online resource allocation problem with budget constraints has a wide range of applications in network science and operation research. In this problem, the decision maker needs to make actions that consume resources to accumulate rewards. Contrary to prior work, we introduce a non-linear and non-separable regularizer to this problem that acts on the total resource consumption. The motivation for introducing the regularizer is allowing the decision maker to trade-off the reward maximization and metrics optimization such as load-balancing and fairness that appears frequently in practical needs. Our goal is to simultaneously maximize additively separable rewards and the value of a non-separable regularizer without violating resource budget constraints. We develop a primal-dual-type online policy for this problem in the online learning setting and confirm its no-regret guarantee and zero constraint violations for stochastic i.i.d. input models. Furthermore, the general convex resource consumption functions allow our model to be more applicable. Numerical experiments demonstrate the theoretical guarantee of our algorithm.