We consider decentralized online convex optimization with time-varying constraints and conduct performance analysis using two stringent metrics: network dynamic regret with respect to the online global solution benchmark, and hard constraint violation that does not allow any compensated violation over time and learners. We propose an efficient algorithm called Constrained Online Learning with Doubly-bounded Queue (COLDQ), which introduces a novel virtual queue that is both lower and upper bounded, allowing tight control of the constraint violation without needing the Slater’s condition. We prove via a new Lyapunov drift analysis that COLDQ providesO(T1+Vx/2) network dynamic regret andO(min{T3+Vx/4;TVg}) hard constraint violation, whereVxandVgcapture the dynamics of the loss and constraint functions. For the first time, the two bounds smoothly approach to the best-knownO(T1/2) regret andO(1) violation, as the dynamics of the losses and constraints diminish, under both centralized and decentralized settings. For strongly convex loss functions, COLDQ providesO(logT) static regret andO(min{T1/2(logT)1/2,TVg}) hard constraint violation. Simulation results based on synthetic and canonical datasets demonstrate that COLDQ substantially outperforms the state-of-the-art approaches for both convex and non-convex loss functions.

We consider online convex optimization with time-varying constraints and conduct performance analysis using two stringent metrics: dynamic regret with respect to the online solution benchmark, and hard constraint violation that does not allow any compensated violation over time. We propose an efficient algorithm called Constrained Online Learning with Doubly-bounded Queue (COLDQ), which introduces a novel virtual queue that is both lower and upper bounded, allowing tight control of the constraint violation without the need for the Slater condition. We prove via a new Lyapunov drift analysis that COLDQ achieves O(T^(1+Vx)/2) dynamic regret and O(T^Vg) hard constraint violation, where Vx and Vg capture the dynamics of the loss and constraint functions. For the first time, the two bounds smoothly approach to the best-known O(T^1/2) regret and O(1) violation, as the dynamics of the losses and constraints diminish. For strongly convex loss functions, COLDQ matches the best-known O(logT) static regret while maintaining the O(T^Vg) hard constraint violation. We further introduce an expert-tracking variation of COLDQ, which achieves the same performance bounds without any prior knowledge of the system dynamics. Simulation results demonstrate that COLDQ outperforms the state-of-the-art approaches.