# Objective-Function Free Multi-Objective Optimization: Rate of Convergence and Performance of an Adagrad-like algorithm

arXiv: https://arxiv.org/abs/2602.05893 · HTML: https://mlsanity.com/paper/2602.05893/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2026.

## Built on by (most cited first, 1 of 1)

- [LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematics](https://mlsanity.com/paper/2602.24173/) (2026)

## Abstract (arXiv)

We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not rely on the dominance property to accept new iterates, which allows for a flexible and function-free optimization framework. New points are obtained using an adaptive stepsize that does not require neither knowledge of Lipschitz constants nor the use of line search procedures. The rate of convergence is analyzed and is shown to be O(1 / √ k+1) with respect to the norm of the common descent direction. The method is extensively validated on a broad class of unconstrained multi-objective problems and simple multi-task learning instances, and compared against a first-order line search algorithm. Additionally, we present a preliminary study of the behavior under noisy multi-objective settings, highlighting the robustness of the method.