Simple and fast algorithm for binary integer and online linear programming

In this paper, we develop a simple and fast online algorithm for solving class of binary integer linear programs (LPs) arisen in general resource allocation problem. The requires only one single pass through the input data is free matrix inversion. It can be viewed as both an approximate LPs LP problems. inspired by equivalent form dual problem relaxed it essentially performs (one-pass) projected stochastic subgradient descent space. We analyze two different models, random permutation, with minimal technical assumptions on data. achieves $$O\left( m \sqrt{n}\right) $$ expected regret under model (m+\log n)\sqrt{n}\right) permutation model, $$O(m \sqrt{n})$$ constraint violation where n number decision variables constraints. enjoys same performance guarantee when generalized to multi-dimensional setting which covers wider range applications. addition, employ notion permutational Rademacher complexity derive bounds earlier algorithms comparison. Both improve bound factor $$\sqrt{m}$$ paying more computational cost. Furthermore, demonstrate how convert possibly infeasible solution feasible randomized procedure. Numerical experiments illustrate applicability effectiveness algorithms.