Low-Bit Distributed Constrained Optimization with Application to Optimal Scheduling and Allocation

Key points

• The algorithm is based on Laplacian-gradient dynamics and preserves the equality (demand) constraint at every iterate, guaranteeing anytime feasibility irrespective of termination time.1
• First, we provide a complete Lyapunov-based convergence analysis for the fixed-step-size regime: the iterates are shown to enter, in at most O(1/\varepsilon^2) iterations, a neighborhood of the optimizer whose radius scales as O(τ) in the decision variable and O(τ^2) in the cost residual, where $τ$ is the step-size.1
• Second, we characterize the invariant set under B-connected, weight-balanced digraphs, strictly weaker than the all-time connectivity and doubly-stochastic weights assumed in most prior work, and show that any odd, sign-preserving nonlinearity yields the same invariant-set and descent structure, with the single-bit protocol being the extreme communication-minimizing instance of a broader nonlinear class.1
• Simulations on economic dispatch (1000 generators) and CPU scheduling (500 servers) demonstrate that the single-bit protocol achieves 5-60 times reduction in total communication cost relative to multi-bit baselines, at the price of a tunable and explicitly bounded optimality gap.1

Sources (1)

• [1]Low-Bit Distributed Constrained Optimization with Application to Optimal Scheduling and Allocation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 17, 03:49 AM

  This paper proposes a distributed resource allocation algorithm in which each agent communicates only the sign of its local cost gradient, a single bit per directed link per iteration.

  The algorithm is based on Laplacian-gradient dynamics and preserves the equality (demand) constraint at every iterate, guaranteeing anytime feasibility irrespective of termination time.

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