Overcoming Deceptiveness in Fitness Optimization with Unsupervised Quality-Diversity

Policy optimization seeks the best solution to a control problem according to an objective or fitness function, serving as a fundamental field of engineering and research with applications in robotics. Traditional optimization methods like reinforcement learning and evolutionary algorithms struggle with deceptive fitness landscapes, where following immediate improvements leads to suboptimal solutions. Quality-diversity (QD) algorithms offer a promising approach by maintaining diverse intermediate solutions as stepping stones for escaping local optima. However, QD algorithms require domain expertise to define hand-crafted features, limiting their applicability where characterizing solution diversity remains unclear. In this paper, we show that unsupervised QD algorithms - specifically the AURORA framework, which learns features from sensory data - efficiently solve deceptive optimization problems without domain expertise. By enhancing AURORA with contrastive learning and periodic extinction events, we propose AURORA-XCon, which outperforms all traditional optimization baselines and matches, in some cases even improving by up to 34%, the best QD baseline with domain-specific hand-crafted features. This work establishes a novel application of unsupervised QD algorithms, shifting their focus from discovering novel solutions toward traditional optimization and expanding their potential to domains where defining feature spaces poses challenges.

Multiscale Neural Operators for Solving Time-Independent PDEs

Time-independent Partial Differential Equations (PDEs) on large meshes pose significant challenges for data-driven neural PDE solvers. We introduce a novel graph rewiring technique to tackle some of these challenges, such as aggregating information across scales and on irregular meshes. Our proposed approach bridges distant nodes, enhancing the global interaction capabilities of GNNs. Our experiments on three datasets reveal that GNN-based methods set new performance standards for time-independent PDEs on irregular meshes. Finally, we show that our graph rewiring strategy boosts the performance of baseline methods, achieving state-of-the-art results in one of the tasks.