Distributed Bandit Online Convex Optimization With Time-Varying Coupled Inequality Constraints

Distributed bandit online convex optimization with time-varying coupled inequality constraints is considered, motivated by a repeated game between group of learners and an adversary. The attempt to minimize sequence global loss functions at the same time satisfy constraint functions, where are across distributed each round. sum local respectively, which adaptively generated revealed in manner, i.e., only values sampling instance, function held privately learner. Both one- two-point feedback studied two corresponding algorithms used learners. We show that sublinear expected regret violation achieved these algorithms, if accumulated variation comparator also grows sublinearly. In particular, we $\mathcal {O}(T^{\theta })$ static {O}(T^{7/4-\theta one-point setting, {O}(T^{\max \lbrace \kappa,1-\kappa \rbrace {O}(T^{1-\kappa /2})$ notation="LaTeX">$\theta \in (3/4,5/6]$ notation="LaTeX">$\kappa (0,1)$ user-defined tradeoff parameters. Finally, tightness theoretical results illustrated numerical simulations simple power grid example, compares proposed existing literature.