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Multi-Task Multi-Behavior MAP-Elites

Anne, Mouret

TL;DR

The paper addresses the challenge of acquiring a diverse set of high-quality reflexes for a family of humanoid fault-recovery tasks. It introduces MTMB-MAP-Elites, which fuses MAP-Elites and Multi-Task MAP-Elites to share solutions across similar tasks and maximize the number of diverse solutions per task, formalized as maximizing $\sum_{i=1}^{n} m_i$ under the constraint that $fitness(T_i,c_i^j)=f_{max}$ and $\mathcal{F}(T_i,c_i^j) \neq \mathcal{F}(T_i,c_i^k)$ for $j \neq k$. The method advances the archive by cross-task crossover among elites, evaluating on random tasks, and updating the map when new behaviors or better fitness are found. Empirical results on a Talos humanoid fault-recovery suite show MTMB-MAP-Elites outperforms Random Search, Grid Search, and Task-Wise MAP-Elites in both solved-task rate and average solutions per solved task, demonstrating the value of cross-task sharing and behavior-space diversity for robust control policies. The work provides a pathway to dataset-driven policy learning for robust wall-contact strategies and highlights practical considerations for simulation-based robotics experimentation and cross-task optimization.

Abstract

We propose Multi-Task Multi-Behavior MAP-Elites, a variant of MAP-Elites that finds a large number of high-quality solutions for a large set of tasks (optimization problems from a given family). It combines the original MAP-Elites for the search for diversity and Multi-Task MAP-Elites for leveraging similarity between tasks. It performs better than three baselines on a humanoid fault-recovery set of tasks, solving more tasks and finding twice as many solutions per solved task.

Multi-Task Multi-Behavior MAP-Elites

TL;DR

The paper addresses the challenge of acquiring a diverse set of high-quality reflexes for a family of humanoid fault-recovery tasks. It introduces MTMB-MAP-Elites, which fuses MAP-Elites and Multi-Task MAP-Elites to share solutions across similar tasks and maximize the number of diverse solutions per task, formalized as maximizing under the constraint that and for . The method advances the archive by cross-task crossover among elites, evaluating on random tasks, and updating the map when new behaviors or better fitness are found. Empirical results on a Talos humanoid fault-recovery suite show MTMB-MAP-Elites outperforms Random Search, Grid Search, and Task-Wise MAP-Elites in both solved-task rate and average solutions per solved task, demonstrating the value of cross-task sharing and behavior-space diversity for robust control policies. The work provides a pathway to dataset-driven policy learning for robust wall-contact strategies and highlights practical considerations for simulation-based robotics experimentation and cross-task optimization.

Abstract

We propose Multi-Task Multi-Behavior MAP-Elites, a variant of MAP-Elites that finds a large number of high-quality solutions for a large set of tasks (optimization problems from a given family). It combines the original MAP-Elites for the search for diversity and Multi-Task MAP-Elites for leveraging similarity between tasks. It performs better than three baselines on a humanoid fault-recovery set of tasks, solving more tasks and finding twice as many solutions per solved task.
Paper Structure (11 sections, 1 equation, 1 figure)

This paper contains 11 sections, 1 equation, 1 figure.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Algorithm
  4. Experiment
  5. Task Space
  6. Command Space
  7. Behavior Space
  8. Fitness Function
  9. Evaluation
  10. Result
  11. Conclusion

Figures (1)

  • Figure 1: Comparison for solving 200 tasks (100 situations with either the right-hand or with both hands) between MTMB-MAP-Elites and three baselines: a random search, a grid search, and MAP-Elites on each task individually. (a) The percentage of tasks solved and (b) the number of solutions per solved task. The line represents the median, the darker shaded area the [25%, 75%] quantiles of the data, and the lighter shaded area [5%, 95%] quantiles on 25 replications. MTMB-MAP-Elites solves more tasks than the best baselines ($+20.8\%$ than Random Search, $+9.9\%$ than Grid-Search, and $+20.7\%$ than Task-Wise MAP-Elites) and more importantly finds more than two times as many solutions per solved task.