This paper proposes a new family of algorithms for online optimisation of composite objectives. The algorithms can be interpreted as the combination of exponentiated gradient and $p$-norm algorithm. Combined with algorithmic ideas of adaptivity and optimism, the proposed algorithms achieve a sequence dependent regret upper bound, matching the best known bounds for sparse target decision variables. Furthermore, the algorithms have efficient implementations for popular composite objectives and constraints, and can be converted to stochastic optimisation algorithms with optimal accelerated rate for smooth objectives.