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ARXIV:2603.18999 · ONLINE OPTIMIZATION · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE
ARXIV:2603.18999ONLINE OPTIMIZATIONSUBMITTED 02 APR · 02:30 UTCFRESHNESS STALERui Chai · arXiv
This paper develops theoretical regret bounds for competitive resource allocation in modular systems with endogenous costs, offering insights into decentralized allocation strategies.
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Pain This paper develops theoretical regret bounds for competitive resource allocation in modular systems with endogenous costs, offering insights into decentralized allocation strategies.
Evidence 0 refs | 0 sources | 17% coverage
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This paper develops theoretical regret bounds for competitive resource allocation in modular systems with endogenous costs, offering insights into decentralized allocation strategies. Unlike standard online optimization, costs are endogenous: they depend on the full…
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…
ScienceToStartup currently rates this 3.0/10 on the public viability pass. 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…
Online Optimization moved forward this cycle; last verified April 2026. Public score 3.0/10.
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This paper develops theoretical regret bounds for competitive resource allocation in modular systems with endogenous costs, offering insights into decentralized allocation strategies.
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10.48550/arXiv.2603.18999This paper develops theoretical regret bounds for competitive resource allocation in modular systems with endogenous costs, offering insights into decentralized allocation strategies.
Abstract
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. Keywords: online learning, regret bounds, resource allocation, endogenous costs, interaction topology, multiplicative weights, modular systems, Wuxing topology
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PROBLEM
This paper develops theoretical regret bounds for competitive resource allocation in modular systems with endogenous costs, offering insights into decentralized allocation strategies. Unlike standard online optimization, costs are endogenous: they depend on the full allocation v...
METHOD
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.
RESULT
ScienceToStartup currently rates this 3.0/10 on the public viability pass. 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)).
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Online Optimization moved forward this cycle; last verified April 2026. Public score 3.0/10.
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This paper develops theoretical regret bounds for competitive resource allocation in modular systems with endogenous costs, offering insights into decentralized allocation strategies. Unlike standard online optimization, costs are endogenous: they depend on the full allocation vector through an interaction matrix W encoding pairwise cooperation and competition.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 3.0/10 on the public viability pass. 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)).
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Online Optimization moved forward this cycle; last verified April 2026. Public score 3.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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This paper develops theoretical regret bounds for competitive resource allocation in modular systems with endogenous costs, offering insights into decentralized allocation strategies.
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