No-regret algorithms for online $k$-submodular maximization

Abstract

We present a polynomial time algorithm for online maximization of k-submodular maximization. For online (nonmonotone) k-submodular maximization, our algorithm achieves a tight approximate factor in an approximate regret. For online monotone k-submodular maximization, our approximate-regret matches to the best-known approximation ratio, which is tight asymptotically as k tends to infinity. Our approach is based on the Blackwell approachability theorem and online linear optimization.