Group Distributionally Robust Optimization with Flexible Sample Queries

• URL: http://arxiv.org/abs/2505.15212v1
• Date: Wed, 21 May 2025 07:41:16 GMT
• Title: Group Distributionally Robust Optimization with Flexible Sample Queries
• Authors: Haomin Bai, Dingzhi Yu, Shuai Li, Haipeng Luo, Lijun Zhang,
• Abstract summary: Group distributionally robust optimization (GDRO) aims to develop models that perform well across $m$ distributions simultaneously.<n>Existing GDRO algorithms can only process a fixed number of samples per iteration, either 1 or $m$.<n>We develop a GDRO algorithm that allows an arbitrary and varying sample size per round, achieving a high-probability optimization error bound of $Oleft(frac1tsqrtsum_j=1t fracmr_jlog mright)$.
• Score: 41.4457693520265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Group distributionally robust optimization (GDRO) aims to develop models that perform well across $m$ distributions simultaneously. Existing GDRO algorithms can only process a fixed number of samples per iteration, either 1 or $m$, and therefore can not support scenarios where the sample size varies dynamically. To address this limitation, we investigate GDRO with flexible sample queries and cast it as a two-player game: one player solves an online convex optimization problem, while the other tackles a prediction with limited advice (PLA) problem. Within such a game, we propose a novel PLA algorithm, constructing appropriate loss estimators for cases where the sample size is either 1 or not, and updating the decision using follow-the-regularized-leader. Then, we establish the first high-probability regret bound for non-oblivious PLA. Building upon the above approach, we develop a GDRO algorithm that allows an arbitrary and varying sample size per round, achieving a high-probability optimization error bound of $O\left(\frac{1}{t}\sqrt{\sum_{j=1}^t \frac{m}{r_j}\log m}\right)$, where $r_t$ denotes the sample size at round $t$. This result demonstrates that the optimization error decreases as the number of samples increases and implies a consistent sample complexity of $O(m\log (m)/\epsilon^2)$ for any fixed sample size $r\in[m]$, aligning with existing bounds for cases of $r=1$ or $m$. We validate our approach on synthetic binary and real-world multi-class datasets.

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