In standard reinforcement learning (RL), a learning agent seeks to optimize the overall reward. However, many key aspects of a desired behavior are more naturally expressed as constraints.

We consider the problem of allocating divisible items among multiple agents, and consider the setting where any agent is allowed to introduce {\emph diversity constraints} on the items they are allocated. We motivate this via settings where the items themselves correspond to user ad slots or task workers with attributes such as race and gender on which the principal seeks to achieve demographic parity. We consider the following question: When an agent expresses diversity constraints into an allocation rule, is the allocation of other agents hurt significantly? If this happens, the cost of introducing such constraints is disproportionately borne by agents who do not benefit from diversity.

We introduce a constraint-programming framework for generating synthetic populations that reproduce target statistics with high precision while enforcing full individual consistency. Unlike data-driven approaches that infer distributions from samples, our method directly encodes aggregated statistics and structural relations, enabling exact control of demographic profiles without requiring any microdata. We validate the approach on official demographic sources and study the impact of distributional deviations on downstream analyses. This work is conducted within the Pollitics project developed by Emotia, where synthetic populations can be queried through large language models to model societal behaviors, explore market and policy scenarios, and provide reproducible decision-grade insights without personal data.

Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the exploration of alternative designs. To address this limitation, we introduce Generative Topology Optimization (GenTO) - a data-free method that trains a neural network to generate structurally compliant shapes and explores diverse solutions through an explicit diversity constraint. The network is trained with a solver-in-the-loop, optimizing the material distribution in each iteration. The trained model produces diverse shapes that closely adhere to the design requirements. We validate GenTO on 2D and 3D TO problems. Our results demonstrate that GenTO produces more diverse solutions than any prior method while maintaining near-optimality and being an order of magnitude faster due to inherent parallelism. These findings open new avenues for engineering and design, offering enhanced flexibility and innovation in structural optimization.

We consider the problem of allocating divisible items among multiple agents, and consider the setting where any agent is allowed to introduce {\emph diversity constraints} on the items they are allocated. We motivate this via settings where the items themselves correspond to user ad slots or task workers with attributes such as race and gender on which the principal seeks to achieve demographic parity. We consider the following question: When an agent expresses diversity constraints into an allocation rule, is the allocation of other agents hurt significantly? If this happens, the cost of introducing such constraints is disproportionately borne by agents who do not benefit from diversity. These are {\emph no negative externality} -- other agents are not hurt -- and {\emph monotonicity} -- the agent enforcing the constraint does not see a large increase in value.

We propose a novel master-slave architecture to solve the top-$K$ combinatorial multi-armed bandits problem with non-linear bandit feedback and diversity constraints, which, to the best of our knowledge, is the first combinatorial bandits setting considering diversity constraints under bandit feedback. Specifically, to efficiently explore the combinatorial and constrained action space, we introduce six slave models with distinguished merits to generate diversified samples well balancing rewards and constraints as well as efficiency. Moreover, we propose teacher learning based optimization and the policy co-training technique to boost the performance of the multiple slave models. The master model then collects the elite samples provided by the slave models and selects the best sample estimated by a neural contextual UCB-based network to make a decision with a trade-off between exploration and exploitation. Thanks to the elaborate design of slave models, the co-training mechanism among slave models, and the novel interactions between the master and slave models, our approach significantly surpasses existing state-of-the-art algorithms in both synthetic and real datasets for recommendation tasks. The code is available at: \url{https://github.com/huanghanchi/Master-slave-Algorithm-for-Top-K-Bandits}.