Momentum-based Distributed Resource Scheduling Optimization Subject to Sector-Bound Nonlinearity and Latency

TL;DR

The paper tackles distributed resource scheduling under a linear coupling constraint, addressing the challenges of communication delays and nonlinear data links. It introduces a momentum-based gradient-tracking algorithm that preserves all-time feasibility and remains robust to sector-bound nonlinear link mappings, even with time-varying, uniformly-connected networks. Theoretical convergence guarantees are provided, including conditions on step sizes, momentum, and delay bounds, along with a delay-tolerant extension. Simulations on synthetic networks and CPU scheduling scenarios demonstrate faster convergence, reduced residuals, and practical applicability to real-time distributed computing environments.

Abstract

This paper proposes an accelerated consensus-based distributed iterative algorithm for resource allocation and scheduling. The proposed gradient-tracking algorithm introduces an auxiliary variable to add momentum towards the optimal state. We prove that this solution is all-time feasible, implying that the coupling constraint always holds along the algorithm iterative procedure; therefore, the algorithm can be terminated at any time. This is in contrast to the ADMM-based solutions that meet constraint feasibility asymptotically. Further, we show that the proposed algorithm can handle possible link nonlinearity due to logarithmically-quantized data transmission (or any sign-preserving odd sector-bound nonlinear mapping). We prove convergence over uniformly-connected dynamic networks (i.e., a hybrid setup) that may occur in mobile and time-varying multi-agent networks. Further, the latency issue over the network is addressed by proposing delay-tolerant solutions. To our best knowledge, accelerated momentum-based convergence, nonlinear linking, all-time feasibility, uniform network connectivity, and handling (possible) time delays are not altogether addressed in the literature. These contributions make our solution practical in many real-world applications.

Figures (7)

• Figure 1: A distributed networked multi-agent optimization/learning setup motivated by cloud-based decentralized computing and parallel processing.
• Figure 2: The log-scale or logarithmic quantizer (with the quantization level $\rho$) is shown in this figure as a strongly sign-preserving sector-bound nonlinearity. The sector-bounds of this nonlinear function are $1 \pm \delta$ as shown in the figure.
• Figure 3: Comparison of the time-evolution of the cost residuals under different resource scheduling solutions in the literature.
• Figure 4: The time-evolution of the cost residuals under different log-scale quantization levels as sector-bound nonlinearity.
• Figure 5: (Left) The time-evolution of the scheduling cost residuals under different momentum rates. (Middle) The time-evolution of the resource states $x_i$ at all agents for $\mu=0.95$. The average of all states remains constant over time implying constraint-feasibility. (Right) The time-evolution of the momentum states $y_i$ at all agents for $\mu=0.95$.

Theorems & Definitions (11)

• Remark 1
• Lemma 1
• Lemma 2
• proof
• Lemma 3
• Lemma 4: Constraint Feasibility
• proof
• Lemma 5: Equilibrium
• proof
• Theorem 1: Convergence