Collision detection is a core component of robotics applications such as simulation, control, and planning. Traditional algorithms like GJK+EPA compute witness points (i.e., the closest or deepest-penetration pairs between two objects) but are inherently non-differentiable, preventing gradient flow and limiting gradient-based optimization in contact-rich tasks such as grasping and manipulation. Recent work introduced efficient first-order randomized smoothing to make witness points differentiable; however, their direction-based formulation is restricted to convex objects and lacks robustness for complex geometries. In this work, we propose a robust and efficient differentiable collision detection framework that supports both convex and concave objects across diverse scales and configurations. Our method introduces distance-based first-order randomized smoothing, adaptive sampling, and equivalent gradient transport for robust and informative gradient computation. Experiments on complex meshes from DexGraspNet and Objaverse show significant improvements over existing baselines. Finally, we demonstrate a direct application of our method for dexterous grasp synthesis to refine the grasp quality. The code is available at https://github.com/JYChen18/DiffCollision.

Understanding how well a deep generative model captures a distribution of high-dimensional data remains an important open challenge. It is especially difficult for certain model classes, such as Generative Adversarial Networks and Diffusion Models, whose models do not admit exact likelihoods. In this work, we demonstrate that generalized empirical likelihood (GEL) methods offer a family of diagnostic tools that can identify many deficiencies of deep generative models (DGMs). We show, with appropriate specification of moment conditions, that the proposed method can identify which modes have been dropped, the degree to which DGMs are mode imbalanced, and whether DGMs sufficiently capture intra-class diversity. We show how to combine techniques from Maximum Mean Discrepancy and Generalized Empirical Likelihood to create not only distribution tests that retain per-sample interpretability, but also metrics that include label information. We find that such tests predict the degree of mode dropping and mode imbalance up to 60% better than metrics such as improved precision/recall. We provide an implementation at https://github.com/deepmind/understanding_deep_generative_models_with_generalized_empirical_likelihood/.

Collision detection appears as a canonical operation in a large range of robotics applications from robot control to simulation, including motion planning and estimation. While the seminal works on the topic date back to the 80s, it is only recently that the question of properly differentiating collision detection has emerged as a central issue, thanks notably to the ongoing and various efforts made by the scientific community around the topic of differentiable physics. Yet, very few solutions have been suggested so far, and only with a strong assumption on the nature of the shapes involved. In this work, we introduce a generic and efficient approach to compute the derivatives of collision detection for any pair of convex shapes, by notably leveraging randomized smoothing techniques which have shown to be particularly adapted to capture the derivatives of non-smooth problems. This approach is implemented in the HPP-FCL and Pinocchio ecosystems, and evaluated on classic datasets and problems of the robotics literature, demonstrating few micro-second timings to compute informative derivatives directly exploitable by many real robotic applications including differentiable simulation.

Modern implicit generative models such as generative adversarial networks (GANs) are generally known to suffer from instability and lack of interpretability as it is difficult to diagnose what aspects of the target distribution are missed by the generative model. In this work, we propose a theoretically grounded solution to these issues by augmenting the GAN's loss function with a kernel-based regularization term that magnifies local discrepancy between the distributions of generated and real samples. The proposed method relies on so-called witness points in the data space which are jointly trained with the generator and provide an interpretable indication of where the two distributions locally differ during the training procedure. In addition, the proposed algorithm is scaled to higher dimensions by learning the witness locations in a latent space of an autoencoder. We theoretically investigate the dynamics of the training procedure, prove that a desirable equilibrium point exists, and the dynamical system is locally stable around this equilibrium. Finally, we demonstrate different aspects of the proposed algorithm by numerical simulations of analytical solutions and empirical results for low and high-dimensional datasets.

Many multi-agent coordination problems can be represented as DCOPs. Motivated by task allocation in disaster response, we extend standard DCOP models to consider uncertain task rewards where the outcome of completing a task depends on its current state, which is randomly drawn from unknown distributions. The goal of solving this problem is to find a solution for all agents that minimizes the overall worst-case loss. This is a challenging problem for centralized algorithms because the search space grows exponentially with the number of agents and is nontrivial for standard DCOP algorithms we have. To address this, we propose a novel decentralized algorithm that incorporates Max-Sum with iterative constraint generation to solve the problem by passing messages among agents. By so doing, our approach scales well and can solve instances of the task allocation problem with hundreds of agents and tasks.

There is much interest in using partially observable Markov decision processes (POMDPs) as a formal model for planning in stochastic domains. This paper is concerned with finding optimal policies for POMDPs. We propose several improvements to incremental pruning, presently the most efficient exact algorithm for solving POMDPs.

Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding optimal policies for POMDPs. It typically takes a large number of iterations to converge. This paper proposes a method for accelerating the convergence of value iteration. The method has been evaluated on an array of benchmark problems and was found to be very effective: It enabled value iteration to converge after only a few iterations on all the test problems.