AGENTIC-SYSTEMSMarch 20, 20261 min read23 views

Regret Bounds for Competitive Resource Allocation with Endogenous Costs

Researchers have established new regret bounds for online resource allocation in modular systems, demonstrating that competitive allocation significantly outperforms traditional methods by leveraging endogenous cost information.

Computer Science > Artificial Intelligence

Title: Regret Bounds for Competitive Resource Allocation with Endogenous Costs

We study online resource allocation among N interacting modules over T rounds. Unlike standard online optimization, costs are endogenous: they depend on the full allocation vector through an interaction matrix W encoding pairwise cooperation and competition.

We analyze three paradigms: (I) uniform allocation (cost-ignorant), (II) gated allocation (cost-estimating), and (III) competitive allocation via multiplicative weights update with interaction feedback (cost-revealing). Our main results establish a strict separation under adversarial sequences with bounded variation: uniform incurs Omega(T) regret, gated achieves O(T^{2/3}), and competitive achieves O(sqrt(T log N)). The performance gap stems from competitive allocation's ability to exploit endogenous cost information revealed through interactions.

We further show that W's topology governs a computation-regret tradeoff. Full interaction (|E|=O(N^2)) yields the tightest bound but highest per-step cost, while sparse topologies (|E|=O(N)) increase regret by at most O(sqrt(log N)) while reducing per-step cost from O(N^2) to O(N). Ring-structured topologies with both cooperative and competitive links - of which the five-element Wuxing topology is canonical - minimize the computation x regret product.

These results provide the first formal regret-theoretic justification for decentralized competitive allocation in modular architectures and establish cost endogeneity as a fundamental challenge distinct from partial observability.

Source: arXiv cs.AI Recent

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