Computable Fairness: Boltzmann-Softmax Control for AI Resource Allocation
For operators of large-scale AI systems, this work provides a practical, scalable method to enforce fairness in resource allocation without sacrificing efficiency.
This paper introduces Computable Fair Division (CFD), a framework that uses the Boltzmann-Softmax function's inverse temperature parameter as a control variable to balance efficiency and fairness in AI resource allocation. The proposed AHC++ algorithm suppresses extreme dominance concentration under shocks while maintaining throughput, with execution time scaling only ~5.5x for a 100x increase in agents.
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