Distributed Online Stochastic-Constrained Convex Optimization With Bandit Feedback.

Area of Science:

• Distributed Optimization
• Multiagent Systems
• Stochastic Convex Optimization

Background:

• Real-world systems often involve dynamic parameters and unknown future conditions.
• Distributed systems require efficient coordination among agents with limited information.
• Online optimization addresses problems where data arrives sequentially.

Purpose of the Study:

• To develop an algorithm for distributed online stochastic convex optimization with time-varying constraints.
• To address scenarios where cost and constraint functions are unknown beforehand.
• To analyze the performance under dynamic network topologies.

Main Methods:

• Development of the adaptive distributed bandit primal-dual algorithm.
• Utilizing bandit feedback with one-point or two-point gradient estimators.
• Designing adaptive step size and regularization sequences without prior knowledge of iteration span T.

Main Results:

• The proposed algorithm achieves sublinear expected dynamic regret.
• Demonstrated sublinear constraint violation under sublinear benchmark sequence drift.
• Validated performance through numerical experiments.

Conclusions:

• The adaptive distributed bandit primal-dual algorithm is effective for dynamic multiagent optimization.
• The method provides theoretical guarantees on regret and constraint violation.
• The approach is robust to time-varying distributions and network structures.