Computable Fairness: Boltzmann-Softmax Control for AI Resource Allocation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910247322386432 |
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| author | Park, Ji-Won Kim, Chae Un |
| author_facet | Park, Ji-Won Kim, Chae Un |
| contents | In large-scale AI systems, allocating scarce resources such as GPU compute time and bandwidth among multiple agents is a critical challenge. Conventional policies focus on efficiency metrics, potentially leading to dominance concentration that undermines system diversity and stability. We propose Computable Fair Division (CFD), a framework that reinterprets the Boltzmann-Softmax function not as a selection tool but as a probabilistic resource allocation mechanism, redefining the inverse temperature parameter $β$ as a computable control variable governing the efficiency-fairness balance. Static analysis reveals a Pareto frontier with a near-optimal Stability Corridor where total loss remains approximately constant across policy weights. In the dynamic setting, AHC++ (Adaptive Hard-Cap Controller++) updates $β$ in real time using the error between observed dominance and a policy-specified target as feedback. Simulations show that AHC++ suppresses extreme dominance concentration under exogenous shocks while tracking fairness targets without substantial throughput degradation. Scalability analysis confirms that a 100x increase in agents yields only approximately 5.5x increase in execution time. Code: https://github.com/entrofy-ai/computable-fairness |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_22827 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computable Fairness: Boltzmann-Softmax Control for AI Resource Allocation Park, Ji-Won Kim, Chae Un Applied Physics Artificial Intelligence Multiagent Systems Performance In large-scale AI systems, allocating scarce resources such as GPU compute time and bandwidth among multiple agents is a critical challenge. Conventional policies focus on efficiency metrics, potentially leading to dominance concentration that undermines system diversity and stability. We propose Computable Fair Division (CFD), a framework that reinterprets the Boltzmann-Softmax function not as a selection tool but as a probabilistic resource allocation mechanism, redefining the inverse temperature parameter $β$ as a computable control variable governing the efficiency-fairness balance. Static analysis reveals a Pareto frontier with a near-optimal Stability Corridor where total loss remains approximately constant across policy weights. In the dynamic setting, AHC++ (Adaptive Hard-Cap Controller++) updates $β$ in real time using the error between observed dominance and a policy-specified target as feedback. Simulations show that AHC++ suppresses extreme dominance concentration under exogenous shocks while tracking fairness targets without substantial throughput degradation. Scalability analysis confirms that a 100x increase in agents yields only approximately 5.5x increase in execution time. Code: https://github.com/entrofy-ai/computable-fairness |
| title | Computable Fairness: Boltzmann-Softmax Control for AI Resource Allocation |
| topic | Applied Physics Artificial Intelligence Multiagent Systems Performance |
| url | https://arxiv.org/abs/2605.22827 |