Sharpness-diversity tradeoff: improving flat ensembles with SharpBalance

TL;DR

This paper explores the relationship between sharpness and diversity in deep ensembles, revealing a trade-off and introducing SharpBalance to optimize both for improved robustness and performance on in-distribution and out-of-distribution data.

Contribution

The paper identifies a sharpness-diversity trade-off in deep ensembles and proposes SharpBalance, a novel training method to better balance these factors for enhanced ensemble robustness.

Findings

SharpBalance improves the sharpness-diversity trade-off.

Ensembles trained with SharpBalance outperform baselines on CIFAR datasets.

Theoretical analysis supports the effectiveness of SharpBalance.

Abstract

Recent studies on deep ensembles have identified the sharpness of the local minima of individual learners and the diversity of the ensemble members as key factors in improving test-time performance. Building on this, our study investigates the interplay between sharpness and diversity within deep ensembles, illustrating their crucial role in robust generalization to both in-distribution (ID) and out-of-distribution (OOD) data. We discover a trade-off between sharpness and diversity: minimizing the sharpness in the loss landscape tends to diminish the diversity of individual members within the ensemble, adversely affecting the ensemble's improvement. The trade-off is justified through our theoretical analysis and verified empirically through extensive experiments. To address the issue of reduced diversity, we introduce SharpBalance, a novel training approach that balances sharpness and diversity within ensembles. Theoretically, we show that our training strategy achieves a better sharpness-diversity trade-off. Empirically, we conducted comprehensive evaluations in various data sets (CIFAR-10, CIFAR-100, TinyImageNet) and showed that SharpBalance not only effectively improves the sharpness-diversity trade-off, but also significantly improves ensemble performance in ID and OOD scenarios.