Robust Learning of a Group DRO Neuron
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914621163569152 |
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| author | Cao, Guyang Li, Shuyao Karmalkar, Sushrut Diakonikolas, Jelena |
| author_facet | Cao, Guyang Li, Shuyao Karmalkar, Sushrut Diakonikolas, Jelena |
| contents | We study the problem of learning a single neuron under standard squared loss in the presence of arbitrary label noise and group-level distributional shifts, for a broad family of covariate distributions. Our goal is to identify a ''best-fit'' neuron parameterized by $\mathbf{w}_*$ that performs well under the most challenging reweighting of the groups. Specifically, we address a Group Distributionally Robust Optimization problem: given sample access to $K$ distinct distributions $\mathcal p_{[1]},\dots,\mathcal p_{[K]}$, we seek to approximate $\mathbf{w}_*$ that minimizes the worst-case objective over convex combinations of group distributions $\boldsymbolλ \in Δ_K$, where the objective is $\sum_{i \in [K]}λ_{[i]}\,\mathbb E_{(\mathbf x,y)\sim\mathcal p_{[i]}}(σ(\mathbf w\cdot\mathbf x)-y)^2 - νd_f(\boldsymbolλ,\frac{1}{K}\mathbf1)$ and $d_f$ is an $f$-divergence that imposes (optional) penalty on deviations from uniform group weights, scaled by a parameter $ν\geq 0$. We develop a computationally efficient primal-dual algorithm that outputs a vector $\widehat{\mathbf w}$ that is constant-factor competitive with $\mathbf{w}_*$ under the worst-case group weighting. Our analytical framework directly confronts the inherent nonconvexity of the loss function, providing robust learning guarantees in the face of arbitrary label corruptions and group-specific distributional shifts. The implementation of the dual extrapolation update motivated by our algorithmic framework shows promise on LLM pre-training benchmarks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_18115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust Learning of a Group DRO Neuron Cao, Guyang Li, Shuyao Karmalkar, Sushrut Diakonikolas, Jelena Machine Learning Data Structures and Algorithms Optimization and Control We study the problem of learning a single neuron under standard squared loss in the presence of arbitrary label noise and group-level distributional shifts, for a broad family of covariate distributions. Our goal is to identify a ''best-fit'' neuron parameterized by $\mathbf{w}_*$ that performs well under the most challenging reweighting of the groups. Specifically, we address a Group Distributionally Robust Optimization problem: given sample access to $K$ distinct distributions $\mathcal p_{[1]},\dots,\mathcal p_{[K]}$, we seek to approximate $\mathbf{w}_*$ that minimizes the worst-case objective over convex combinations of group distributions $\boldsymbolλ \in Δ_K$, where the objective is $\sum_{i \in [K]}λ_{[i]}\,\mathbb E_{(\mathbf x,y)\sim\mathcal p_{[i]}}(σ(\mathbf w\cdot\mathbf x)-y)^2 - νd_f(\boldsymbolλ,\frac{1}{K}\mathbf1)$ and $d_f$ is an $f$-divergence that imposes (optional) penalty on deviations from uniform group weights, scaled by a parameter $ν\geq 0$. We develop a computationally efficient primal-dual algorithm that outputs a vector $\widehat{\mathbf w}$ that is constant-factor competitive with $\mathbf{w}_*$ under the worst-case group weighting. Our analytical framework directly confronts the inherent nonconvexity of the loss function, providing robust learning guarantees in the face of arbitrary label corruptions and group-specific distributional shifts. The implementation of the dual extrapolation update motivated by our algorithmic framework shows promise on LLM pre-training benchmarks. |
| title | Robust Learning of a Group DRO Neuron |
| topic | Machine Learning Data Structures and Algorithms Optimization and Control |
| url | https://arxiv.org/abs/2601.18115 |