# RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning

arXiv: https://arxiv.org/abs/2309.02250 · HTML: https://mlsanity.com/paper/2309.02250/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 42 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## Builds on (most cited first, 2 of 2)

- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Federated Accelerated Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08950/) (2020)

## Built on by (most cited first, 15 of 15)

- [Enhancing Multiview Synergy: Robust Learning by Exploiting the Wave Loss Function with Consensus and Complementarity Principles](https://mlsanity.com/paper/2408.06819/) (2024)
- [Advancing Supervised Learning with the Wave Loss Function: A Robust and Smooth Approach](https://mlsanity.com/paper/2404.18101/) (2024)
- [Advancing RVFL networks: Robust classification with the HawkEye loss function](https://mlsanity.com/paper/2410.00510/) (2024)
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- [Enhanced Feature Based Granular Ball Twin Support Vector Machine](https://mlsanity.com/paper/2410.05786/) (2024)
- [GL-TSVM: A robust and smooth twin support vector machine with guardian loss function](https://mlsanity.com/paper/2408.16336/) (2024)
- [Flexi-Fuzz least squares SVM for Alzheimer's diagnosis: Tackling noise, outliers, and class imbalance](https://mlsanity.com/paper/2410.14207/) (2024)
- [Enhancing Imbalance Learning: A Novel Slack-Factor Fuzzy SVM Approach](https://mlsanity.com/paper/2411.17128/) (2024)
- [Single-weight Model Editing for Post-hoc Spurious Correlation Neutralization](https://mlsanity.com/paper/2501.14182/) (2025)
- [CI-RKM: A Class-Informed Approach to Robust Restricted Kernel Machines](https://mlsanity.com/paper/2504.11476/) (2025)
- [Stability as a Liability:Systematic Breakdown of Linguistic Structure in LLMs](https://mlsanity.com/paper/2601.18588/) (2026)
- [Designing a Robust, Bounded, and Smooth Loss Function for Improved Supervised Learning](https://mlsanity.com/paper/2602.06858/) (2026)
- [Sparse and robust geometric twin support vector machine via asymmetric RoBoSS loss function](https://mlsanity.com/paper/2608.11567/) (2026)
- [Robust Broad Learning System with Wave Loss for Classification under Data Uncertainty](https://mlsanity.com/paper/2608.29983/) (2026)
- [IFW-BLS: Dual-Robust Broad Learning System with Intuitionistic Fuzzy Wave Loss](https://mlsanity.com/paper/2609.02422/) (2026)

## Abstract (arXiv)

In the domain of machine learning, the significance of the loss function is paramount, especially in supervised learning tasks. It serves as a fundamental pillar that profoundly influences the behavior and efficacy of supervised learning algorithms. Traditional loss functions, though widely used, often struggle to handle outlier-prone and high-dimensional data, resulting in suboptimal outcomes and slow convergence during training. In this paper, we address the aforementioned constraints by proposing a novel robust, bounded, sparse, and smooth (RoBoSS) loss function for supervised learning. Further, we incorporate the RoBoSS loss within the framework of support vector machine (SVM) and introduce a new robust algorithm named LRoBoSS-SVM. For the theoretical analysis, the classification-calibrated property and generalization ability are also presented. These investigations are crucial for gaining deeper insights into the robustness of the RoBoSS loss function in classification problems and its potential to generalize well to unseen data. To validate the potency of the proposed LRoBoSS-SVM, we assess it on 88 benchmark datasets from KEEL and UCI repositories. Further, to rigorously evaluate its performance in challenging scenarios, we conducted an assessment using datasets intentionally infused with outliers and label noise. Additionally, to exemplify the effectiveness of LRoBoSS-SVM within the biomedical domain, we evaluated it on two medical datasets: the electroencephalogram (EEG) signal dataset and the breast cancer (BreaKHis) dataset. The numerical results substantiate the superiority of the proposed LRoBoSS-SVM model, both in terms of its remarkable generalization performance and its efficiency in training time.