$φ$-Balancing for Mixture-of-Experts Training

Lizhang Chen, Jonathan Li, Qi Wang, Runlong Liao, Shuozhe Li, Chen Liang, Ni Lao, Qiang Liu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:15228-15245, 2026.

Abstract

Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on noisy mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $\phi$-balancing, a principled framework that directly targets population-level expert balance by minimizing a strictly convex, symmetric, and differentiable potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $\phi$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26br, title = {$φ$-Balancing for Mixture-of-Experts Training}, author = {Chen, Lizhang and Li, Jonathan and Wang, Qi and Liao, Runlong and Li, Shuozhe and Liang, Chen and Lao, Ni and Liu, Qiang}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {15228--15245}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26br/chen26br.pdf}, url = {https://proceedings.mlr.press/v306/chen26br.html}, abstract = {Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on noisy mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $\phi$-balancing, a principled framework that directly targets population-level expert balance by minimizing a strictly convex, symmetric, and differentiable potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $\phi$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.} }
Endnote
%0 Conference Paper %T $φ$-Balancing for Mixture-of-Experts Training %A Lizhang Chen %A Jonathan Li %A Qi Wang %A Runlong Liao %A Shuozhe Li %A Chen Liang %A Ni Lao %A Qiang Liu %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26br %I PMLR %P 15228--15245 %U https://proceedings.mlr.press/v306/chen26br.html %V 306 %X Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on noisy mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $\phi$-balancing, a principled framework that directly targets population-level expert balance by minimizing a strictly convex, symmetric, and differentiable potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $\phi$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.
APA
Chen, L., Li, J., Wang, Q., Liao, R., Li, S., Liang, C., Lao, N. & Liu, Q.. (2026). $φ$-Balancing for Mixture-of-Experts Training. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:15228-15245 Available from https://proceedings.mlr.press/v306/chen26br.html.

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