Trading regret for efficiency online convex optimization with long term constraints
Bandit convex optimization is a special case of online convex optimization with regret. Zinkevich (2003) presents a strategy based on gradient descent that 1Both of these results are novel but their proof is omitted due to space constraints . The algorithms we propose are efficient, with the computational complexities Trading Regret for Efficiency: Online Convex Optimization ... • A convex-concave formulation of online convex optimization with long term constraints, and an efficient algorithm based on OGD that attains a regret bound of O(T1/2), and O(T3/4) violation of the constraints. • A modified OGD based algorithm for online convex optimization with long term constraints