# Composite convex minimization involving self-concordant-like cost functions

arXiv: https://arxiv.org/abs/1502.01068 · HTML: https://mlsanity.com/paper/1502.01068/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2015.

## Built on by (most cited first, 12 of 12)

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- [UCB-based Algorithms for Multinomial Logistic Regression Bandits](https://mlsanity.com/paper/2103.11489/) (2021)
- [Efficient Methods for Online Multiclass Logistic Regression](https://mlsanity.com/paper/2110.03020/) (2021)
- [Provably Efficient Reinforcement Learning with Multinomial Logit Function Approximation](https://mlsanity.com/paper/2405.17061/) (2024)
- [Exponential Weights Algorithms for Selective Learning](https://mlsanity.com/paper/2106.15662/) (2021)
- [Scalable Frank-Wolfe on Generalized Self-concordant Functions via Simple Steps](https://mlsanity.com/paper/2105.13913/) (2021)
- [Layer-wise Adaptive Step-Sizes for Stochastic First-Order Methods for Deep Learning](https://mlsanity.com/paper/2305.13664/) (2023)
- [Tractable Multinomial Logit Contextual Bandits with Non-Linear Utilities](https://mlsanity.com/paper/2601.06913/) (2026)
- [Efficient Multinomial Logistic Bandit via Frequent Directions](https://mlsanity.com/paper/2606.11968/) (2026)

## Abstract (arXiv)

The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept has heretofore remained unexploited in convex optimization. To this end, we develop a variable metric framework of minimizing the sum of a "simple" convex function and a self-concordant-like function. We introduce a new analytic step-size selection procedure and prove that the basic gradient algorithm has improved convergence guarantees as compared to "fast" algorithms that rely on the Lipschitz gradient property. Our numerical tests with real-data sets shows that the practice indeed follows the theory.