Multi-task optimization is a powerful approach for solving a large number of tasks in parallel. However, existing algorithms face distinct limitations: Population-based methods scale poorly and remain underexplored for large task sets. Approaches that do scale beyond a thousand tasks are mostly MAP-Elites variants and rely on a fixed, discretized archive that disregards the topology of the task space. We introduce MONET (Multi-Task Optimization over Networks of Tasks), a multi-task optimization algorithm that models the task space as a graph: tasks are nodes, and edges connect tasks in the task parameter space. This representation enables knowledge transfer between tasks and remains tractable for high-dimensional problems while exploiting the topology of the task space. MONET combines social learning, which generates candidates from neighboring nodes via crossover, with individual learning, which refines a node's own solution independently via mutation. We evaluate MONET on four domains (archery, arm, and cartpole with 5,000 tasks each; hexapod with 2,000 tasks) and show that it matches or exceeds the performance of existing MAP-Elites-based baselines across all four domains.

翻译：多任务优化是一种并行求解大量任务的有效方法。然而，现有算法面临显著局限性：基于种群的方法扩展性差，且在大规模任务集上的研究尚不充分。能够扩展到数千个任务的方法主要基于MAP-Elites变体，依赖固定的离散化存档，忽略了任务空间的拓扑结构。我们提出MONET（任务网络中的多任务优化），这是一种将任务空间建模为图的多任务优化算法：任务作为节点，边连接任务参数空间中的相邻任务。这种表示方法既能在高维问题中保持可处理性，又能利用任务空间的拓扑结构实现任务间的知识迁移。MONET结合了社会学习（通过交叉操作从邻近节点生成候选解）与个体学习（通过变异操作独立优化节点自身解）。我们在四个领域（弓箭、机械臂、小车倒立摆各5000个任务；六足机器人2000个任务）上评估MONET，结果表明其在所有四个领域中均达到或超越现有基于MAP-Elites的基线方法。