# Parametric-Task MAP-Elites

arXiv: https://arxiv.org/abs/2402.01275 · HTML: https://mlsanity.com/paper/2402.01275/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 66 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [An Introduction to Deep Reinforcement Learning](https://mlsanity.com/paper/1811.12560/) (2018)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space](https://mlsanity.com/paper/1912.02400/) (2019)
- [Differentiable Quality Diversity](https://mlsanity.com/paper/2106.03894/) (2021)
- [Active Learning of Inverse Models with Intrinsically Motivated Goal Exploration in Robots](https://mlsanity.com/paper/1301.4862/) (2013)
- [Covariance Matrix Adaptation MAP-Annealing](https://mlsanity.com/paper/2205.10752/) (2022)
- [Quality Diversity for Multi-task Optimization](https://mlsanity.com/paper/2003.04407/) (2020)
- [Half a Dozen Real-World Applications of Evolutionary Multitasking, and More](https://mlsanity.com/paper/2109.13101/) (2021)
- [Strategies for Using Proximal Policy Optimization in Mobile Puzzle Games](https://mlsanity.com/paper/2007.01542/) (2020)
- [Multi-Task Multi-Behavior MAP-Elites](https://mlsanity.com/paper/2305.01264/) (2023)

## Built on by (most cited first, 4 of 4)

- [(θl, θu)-Parametric Multi-Task Optimization: Joint Search in Solution and Infinite Task Spaces](https://mlsanity.com/paper/2503.08394/) (2025)
- [Beyond Single-Model Optimization: Preserving Plasticity in Continual Reinforcement Learning](https://mlsanity.com/paper/2604.15414/) (2026)
- [Multi-Task Optimization over Networks of Tasks](https://mlsanity.com/paper/2604.21991/) (2026)
- [Contextual Quality-Diversity Evolutionary Reinforcement Learning for HVAC Control in Tropical Commercial Buildings](https://mlsanity.com/paper/2608.11324/) (2026)

## Abstract (arXiv)

Optimizing a set of functions simultaneously by leveraging their similarity is called multi-task optimization. Current black-box multi-task algorithms only solve a finite set of tasks, even when the tasks originate from a continuous space. In this paper, we introduce Parametric-Task MAP-Elites (PT-ME), a new black-box algorithm for continuous multi-task optimization problems. This algorithm (1) solves a new task at each iteration, effectively covering the continuous space, and (2) exploits a new variation operator based on local linear regression. The resulting dataset of solutions makes it possible to create a function that maps any task parameter to its optimal solution. We show that PT-ME outperforms all baselines, including the deep reinforcement learning algorithm PPO on two parametric-task toy problems and a robotic problem in simulation.