A.1 Multiple data matrices A combinatorial optimization problem can be presented with multiple (f) relationship features between two groups of items. In FFSP, for example, a production cost could be different for each process that one has to take into account for scheduling in addition to the processing time for each pair of the job and the machine. "Trainable element-wise function" block in Figure A.1 is now an MLP with f + 1 input nodes and 1 output node. A.2 Alternative encoding sequences Equation (2) in the main text describes the application of F The bold line indicates the change from the original. A.3 Alternatives to one-hot initial node embeddings For initial node representations of nodes in group B, one only needs mutually distinct-enough N We have chosen to present our model with onehot vectors because it is the simplest to implement this way.

In the natural world, life has found innumerable ways to survive and often thrive. Between and even within species, each individual is in some manner unique, and this diversity lends adaptability and robustness to life. In this work, we aim to learn a space of diverse and high-reward policies in a given environment. To this end, we introduce a generative model of policies for reinforcement learning, which maps a low-dimensional latent space to an agent policy space. Our method enables learning an entire population of agent policies, without requiring the use of separate policy parameters. Just as real world populations can adapt and evolve via natural selection, our method is able to adapt to changes in our environment solely by selecting for policies in latent space. We test our generative model's capabilities in a variety of environments, including an open-ended grid-world and a two-player soccer environment.

Multiobjective optimization (MOO) plays a critical role in various real-world domains. A major challenge therein is generating K uniform Pareto-optimal solutions to approximate the entire Pareto front. To address this issue, this paper firstly introduces fill distance to evaluate the K design points, which provides a quantitative metric for the representativeness of the design. However, directly specifying the optimal design that minimizes the fill distance is nearly intractable due to the involved nested min max min problem structure. To address this, we propose a surrogate "max-packing" design for the fill distance design, which is easier to optimize and leads to a rate-optimal design with a fill distance at most 4 the minimum value. Extensive experiments on synthetic and real-world benchmarks demonstrate that our proposed paradigm efficiently produces highquality, representative solutions and outperforms baseline MOO methods.

Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, fairness, robustness, and more. Unlike single-objective optimization, which aggregates objectives into a scalar through weighted sums, MOPs focus on generating specific or diverse Pareto solutions and learning the entire Pareto set directly. Existing MOP benchmarks primarily focus on evolutionary algorithms, which are zeroth-order or meta-heuristic methods that fail to leverage higher-order objective information and cannot scale to large models. To address these challenges, we introduce LibMOON, the first multiobjective optimization library supporting state-of-the-art gradient-based methods, offering a fair and comprehensive benchmark, and open-sourced for the community.

Neural architecture search (NAS) finds high performing networks for a given task. Yet the results of NAS are fairly prosaic; they did not e.g.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/