Johnny R. Zhang

Johnny R. Zhang, Gaoyuan Du, Qianyi Sun et al.

AI data centers are increasingly becoming tightly coupled compute--energy systems, where workload placement, cooling demand, electricity procurement, storage operation, and carbon emissions interact over time. This paper studies carbon-aware compute--power scheduling for geographically distributed AI data centers with microgrid prosumer capabilities. We propose a mixed-integer linear programming (MILP) framework that jointly schedules rigid training jobs, routes elastic inference workloads, dispatches local generation and battery storage, and manages bidirectional grid interaction under latency, continuity, power-balance, and carbon-budget constraints. The model captures two key features of emerging AI infrastructure: heterogeneous workload flexibility and site-level energy prosumer operation. Experiments on synthetic yet practically motivated instances show that the proposed joint MILP substantially improves total operational benefit over compute-only and energy-only baselines while reducing emissions. The results further indicate that inference-routing flexibility is a major source of value, battery storage provides useful temporal flexibility, and local-generation-rich settings are particularly favorable. The framework provides a tractable optimization abstraction for sustainable and grid-interactive AI data centers.

Johnny R. Zhang, Xiaomei Mi, Gaoyuan Du et al.

Stochastic optimization powers the scalability of modern artificial intelligence, spanning machine learning, deep learning, reinforcement learning, and large language model training. Yet, existing theory remains largely confined to Hilbert spaces, relying on inner-product frameworks and orthogonality. This paradigm fails to capture non-Euclidean settings, such as mirror descent on simplices, Bregman proximal methods for sparse learning, natural gradient descent in information geometry, or Kullback--Leibler-regularized language model training. Unlike Euclidean-based Hilbert-space methods, this approach embraces general Banach spaces. This work introduces a pioneering Banach--Bregman framework for stochastic iterations, establishing Bregman geometry as a foundation for next-generation optimization. It (i) provides a unified template via Bregman projections and Bregman--Fejer monotonicity, encompassing stochastic approximation, mirror descent, natural gradient, adaptive methods, and mirror-prox; (ii) establishes super-relaxations ($λ> 2$) in non-Hilbert settings, enabling flexible geometries and elucidating their acceleration effect; and (iii) delivers convergence theorems spanning almost-sure boundedness to geometric rates, validated on synthetic and real-world tasks. Empirical studies across machine learning (UCI benchmarks), deep learning (e.g., Transformer training), reinforcement learning (actor--critic), and large language models (WikiText-2 with distilGPT-2) show up to 20% faster convergence, reduced variance, and enhanced accuracy over classical baselines. These results position Banach--Bregman geometry as a cornerstone unifying optimization theory and practice across core AI paradigms.