Generative Adversarial Networks (GANs) are unsupervised models designed to learn and replicate a target distribution. The vanilla versions of these models can be extended to more controllable models. Conditional Generative Adversarial Networks (CGANs) extend vanilla GANs by conditioning both the generator and discriminator on some additional information (labels). Controllable models based on complementary learning, such as Rumi-GAN, have been introduced. Rumi-GANs leverage negative examples to enhance the generator's ability to learn positive examples. We evaluate the performance of two controllable GAN variants, CGAN and Rumi-GAN, in generating game levels targeting specific constraints of interest: playability and controllability. This evaluation is conducted under two scenarios: with and without the inclusion of negative examples. The goal is to determine whether incorporating negative examples helps the GAN models avoid generating undesirable outputs. Our findings highlight the strengths and weaknesses of each method in enforcing the generation of specific conditions when generating outputs based on given positive and negative examples.

Deep Reinforcement Learning (DRL) algorithms have achieved great success in solving many challenging tasks while their black-box nature hinders interpretability and real-world applicability, making it difficult for human experts to interpret and understand DRL policies. Existing works on interpretable reinforcement learning have shown promise in extracting decision tree (DT) based policies from DRL policies with most focus on the single-agent settings while prior attempts to introduce DT policies in multi-agent scenarios mainly focus on heuristic designs which do not provide any quantitative guarantees on the expected return. In this paper, we establish an upper bound on the return gap between the oracle expert policy and an optimal decision tree policy. This enables us to recast the DT extraction problem into a novel non-euclidean clustering problem over the local observation and action values space of each agent, with action values as cluster labels and the upper bound on the return gap as clustering loss. Both the algorithm and the upper bound are extended to multi-agent decentralized DT extractions by an iteratively-grow-DT procedure guided by an action-value function conditioned on the current DTs of other agents. Further, we propose the Return-Gap-Minimization Decision Tree (RGMDT) algorithm, which is a surprisingly simple design and is integrated with reinforcement learning through the utilization of a novel Regularized Information Maximization loss. Evaluations on tasks like D4RL show that RGMDT significantly outperforms heuristic DT-based baselines and can achieve nearly optimal returns under given DT complexity constraints (e.g., maximum number of DT nodes).

Fr\'echet regression is becoming a mainstay in modern data analysis for analyzing non-traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such as continuous monitoring and imaging data. Fr\'echet regression utilizes the pairwise distances between the random objects, which makes the choice of metric crucial in the estimation. In this paper, existing dimension reduction methods for Fr\'echet regression are reviewed, and the effect of metric choice on the estimation of the dimension reduction subspace is explored for the regression between random responses and Euclidean predictors. Extensive numerical studies illustrate how different metrics affect the central and central mean space estimators. Two real applications involving analysis of brain connectivity networks of subjects with and without Parkinson's disease and an analysis of the distributions of glycaemia based on continuous glucose monitoring data are provided, to demonstrate how metric choice can influence findings in real applications.

With the explosive growth of Internet data, users are facing the problem of information overload, which makes it a challenge to efficiently obtain the required resources. Recommendation systems have emerged in this context. By filtering massive amounts of information, they provide users with content that meets their needs, playing a key role in scenarios such as advertising recommendation and product recommendation. However, traditional click-through rate prediction and TOP-K recommendation mechanisms are gradually unable to meet the recommendations needs in modern life scenarios due to high computational complexity, large memory consumption, long feature selection time, and insufficient feature interaction. This paper proposes a recommendations system model based on a separation embedding cross-network. The model uses an embedding neural network layer to transform sparse feature vectors into dense embedding vectors, and can independently perform feature cross operations on different dimensions, thereby improving the accuracy and depth of feature mining. Experimental results show that the model shows stronger adaptability and higher prediction accuracy in processing complex data sets, effectively solving the problems existing in existing models.

Heterogeneous graphs are present in various domains, such as social networks, recommendation systems, and biological networks. Unlike homogeneous graphs, heterogeneous graphs consist of multiple types of nodes and edges, each representing different entities and relationships. Generating realistic heterogeneous graphs that capture the complex interactions among diverse entities is a difficult task due to several reasons. The generator has to model both the node type distribution along with the feature distribution for each node type. In this paper, we look into solving challenges in heterogeneous graph generation, by employing a two phase hierarchical structure, wherein the first phase creates a skeleton graph with node types using a prior diffusion based model and in the second phase, we use an encoder and a sampler structure as generator to assign node type specific features to the nodes. A discriminator is used to guide training of the generator and feature vectors are sampled from a node feature pool. We conduct extensive experiments with subsets of IMDB and DBLP datasets to show the effectiveness of our method and also the need for various architecture components.

An ideal winner in such an election is a Condorcet winner, a candidate that "beats" any other candidate in a pairwise voting contest. Formally, i C is a Condorcet winner if, for every candidate j C\{i}, more than half of the voters prefer i over j. To avoid ties, we assume the number n of voters is odd. Unfortunately, it is easy to construct elections where a Condorcet winner does not exist; indeed typically there is no Condorcet winner. Given this, Elkind, Lang and Saffidine [12] proposed a relaxation where, rather than a single winning candidate, we desire a set of winning candidates that collectively beats any other candidate. Specifically, a set of candidates S C is a Condorcet winning set if, for every candidate j C \S, more than half of the voters prefer some (voter-dependent) candidate in S to j. Elkind et al. [12] showed that a Condorcet winning set always exists provided we allow the winning set to be large enough.

For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two primary drawbacks: they either lack the ability to model high-order correlations among variables while maintaining computationally tractable inference, or they do not allow to explicitly model known correlations. To address this shortcoming, we introduce'Graph Structured Prediction Energy Networks,' for which we develop inference techniques that allow to both model explicit local and implicit higher-order correlations while maintaining tractability of inference. We apply the proposed method to tasks from the natural language processing and computer vision domain and demonstrate its general utility.

Structured prediction of tree-shaped objects is heavily studied under the name of syntactic dependency parsing. Current practice based on maximum likelihood or margin is either agnostic to or inconsistent with the evaluation loss. Risk minimization alleviates the discrepancy between training and test objectives but typically induces a non-convex problem. These approaches adopt explicit regularization to combat overfitting without probabilistic interpretation. We propose a moment-based distributionally robust optimization approach for tree structured prediction, where the worst-case expected loss over a set of distributions within bounded moment divergence from the empirical distribution is minimized.

In structured output prediction tasks, labeling ground-truth training output is often expensive. However, for many tasks, even when the true output is unknown, we can evaluate predictions using a scalar reward function, which may be easily assembled from human knowledge or non-differentiable pipelines. But searching through the entire output space to find the best output with respect to this reward function is typically intractable. In this paper, we instead use efficient truncated randomized search in this reward function to train structured prediction energy networks (SPENs), which provide efficient test-time inference using gradient-based search on a smooth, learned representation of the score landscape, and have previously yielded state-of-the-art results in structured prediction. In particular, this truncated randomized search in the reward function yields previously unknown local improvements, providing effective supervision to SPENs, avoiding their traditional need for labeled training data.

Consider a nonparametric contextual multi-arm bandit problem where each arm a \in [K] is associated to a nonparametric reward function f_a: [0,1] \to \mathbb{R} mapping from contexts to the expected reward. Suppose that there is a large set of arms, yet there is a simple but unknown structure amongst the arm reward functions, e.g. We present a novel algorithm which learns data-driven similarities amongst the arms, in order to implement adaptive partitioning of the context-arm space for more efficient learning. We provide regret bounds along with simulations that highlight the algorithm's dependence on the local geometry of the reward functions.