Distribution-Dependent Rates for Multi-Distribution Learning

• URL: http://arxiv.org/abs/2312.13130v1
• Date: Wed, 20 Dec 2023 15:50:16 GMT
• Title: Distribution-Dependent Rates for Multi-Distribution Learning
• Authors: Rafael Hanashiro, Patrick Jaillet
• Abstract summary: Recent multi-distribution learning framework tackles this objective in a dynamic interaction with the environment. We provide distribution-dependent guarantees in the MDL regime, that scale with suboptimality gaps and result in superior dependence on the sample size. We devise an adaptive optimistic algorithm, LCB-DR, that showcases enhanced dependence on the gaps, mirroring the contrast between uniform and optimistic allocation in the multi-armed bandit literature.
• Score: 26.38831409926518
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To address the needs of modeling uncertainty in sensitive machine learning applications, the setup of distributionally robust optimization (DRO) seeks good performance uniformly across a variety of tasks. The recent multi-distribution learning (MDL) framework tackles this objective in a dynamic interaction with the environment, where the learner has sampling access to each target distribution. Drawing inspiration from the field of pure-exploration multi-armed bandits, we provide distribution-dependent guarantees in the MDL regime, that scale with suboptimality gaps and result in superior dependence on the sample size when compared to the existing distribution-independent analyses. We investigate two non-adaptive strategies, uniform and non-uniform exploration, and present non-asymptotic regret bounds using novel tools from empirical process theory. Furthermore, we devise an adaptive optimistic algorithm, LCB-DR, that showcases enhanced dependence on the gaps, mirroring the contrast between uniform and optimistic allocation in the multi-armed bandit literature.

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