Constrained distributed online convex optimization with bandit feedback for unbalanced digraphs

In this study, a distributed primal‐dual bandit feedback method for online convex optimization with time‐varying coupled inequality constraints on unbalanced directed graphs is proposed. A multiagent network is considered in which agents exchange the estimations of the dual optimizer and the scaling variable with their neighbors. The scaling variable is used to resolve the bias of the estimations caused by a directed communication network. Each agent does not have prior knowledge of the loss function, and its value at a queried point is sequentially disclosed to each agent. Each agent performs a projected subgradient‐based primal‐dual algorithm to estimate the optimal solution. It is confirmed that both the expected dynamic regret of the loss function and the cumulative error of the constraint violation achieve sublinearity using the proposed online algorithm with the two‐point bandit feedback. Regret analysis for the distributed PEV charging problem with and without the bandit feedback.