Safe and Efficient Online Convex Optimization with Linear Budget Constraints and Partial Feedback
This work addresses safe and efficient decision-making in constrained online learning, with applications like energy management in data centers.
The paper tackles online convex optimization with unknown linear budget constraints and partial feedback, proposing the SELO algorithm that achieves O(√T) regret and zero cumulative constraint violation.
This paper studies online convex optimization with unknown linear budget constraints, where only the gradient information of the objective and the bandit feedback of constraint functions are observed. We propose a safe and efficient Lyapunov-optimization algorithm (SELO) that can achieve an $O(\sqrt{T})$ regret and zero cumulative constraint violation. The result also implies SELO achieves $O(\sqrt{T})$ regret when the budget is hard and not allowed to be violated. The proposed algorithm is computationally efficient as it resembles a primal-dual algorithm where the primal problem is an unconstrained, strongly convex and smooth problem, and the dual problem has a simple gradient-type update. The algorithm and theory are further justified in a simulated application of energy-efficient task processing in distributed data centers.