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Task and Motion Planning (TAMP) algorithms can generate plans that combine logic and motion aspects for robots. However, these plans are sensitive to interference and control errors. To make TAMP more applicable in real-world, we propose the modular multi-level replanning TAMP framework(MMRF), blending the probabilistic completeness of sampling-based TAMP algorithm with the robustness of reactive replanning. MMRF generates an nominal plan from the initial state, then dynamically reconstructs this nominal plan in real-time, reorders robot manipulations. Following the logic-level adjustment, GMRF will try to replan a new motion path to ensure the updated plan is feasible at the motion level. Finally, we conducted real-world experiments involving stack and rearrange task domains. The result demonstrate MMRF's ability to swiftly complete tasks in scenarios with varying degrees of interference.

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like conjugate gradients (CG). However, as datasets increase in magnitude, the kernel matrices become increasingly ill-conditioned and still require $\mathcal{O}(n^2)$ space without partitioning. Thus, while CG increases the size of datasets GPs can be trained on, modern datasets reach scales beyond its applicability. In this work, we propose an iterative method which only accesses subblocks of the kernel matrix, effectively enabling mini-batching. Our algorithm, based on alternating projection, has $\mathcal{O}(n)$ per-iteration time and space complexity, solving many of the practical challenges of scaling GPs to very large datasets. Theoretically, we prove the method enjoys linear convergence. Empirically, we demonstrate its fast convergence in practice and robustness to ill-conditioning. On large-scale benchmark datasets with up to four million data points, our approach accelerates GP training and inference by speed-up factors up to $27\times$ and $72 \times$, respectively, compared to CG.

In dynamic submodular maximization, the goal is to maintain a high-value solution over a sequence of element insertions and deletions with a fast update time. Motivated by large-scale applications and the fact that dynamic data often exhibits patterns, we ask the following question: can predictions be used to accelerate the update time of dynamic submodular maximization algorithms? We consider the model for dynamic algorithms with predictions where predictions regarding the insertion and deletion times of elements can be used for preprocessing. Our main result is an algorithm with an $O(poly(\log \eta, \log w, \log k))$ amortized update time over the sequence of updates that achieves a $1/2 - \epsilon$ approximation in expectation for dynamic monotone submodular maximization under a cardinality constraint $k$, where the prediction error $\eta$ is the number of elements that are not inserted and deleted within $w$ time steps of their predicted insertion and deletion times. This amortized update time is independent of the length of the stream and instead depends on the prediction error.

Reinforcement learning with human feedback (RLHF) is an emerging paradigm to align models with human preferences. Typically, RLHF aggregates preferences from multiple individuals who have diverse viewpoints that may conflict with each other. Our work \textit{initiates} the theoretical study of multi-party RLHF that explicitly models the diverse preferences of multiple individuals. We show how traditional RLHF approaches can fail since learning a single reward function cannot capture and balance the preferences of multiple individuals. To overcome such limitations, we incorporate meta-learning to learn multiple preferences and adopt different social welfare functions to aggregate the preferences across multiple parties. We focus on the offline learning setting and establish sample complexity bounds, along with efficiency and fairness guarantees, for optimizing diverse social welfare functions such as Nash, Utilitarian, and Leximin welfare functions. Our results show a separation between the sample complexities of multi-party RLHF and traditional single-party RLHF. Furthermore, we consider a reward-free setting, where each individual's preference is no longer consistent with a reward model, and give pessimistic variants of the von Neumann Winner based on offline preference data. Taken together, our work showcases the advantage of multi-party RLHF but also highlights its more demanding statistical complexity.

We propose a hybrid model predictive control algorithm, consensus complementarity control (C3), for systems that make and break contact with their environment. Many state-of-the-art controllers for tasks which require initiating contact with the environment, such as locomotion and manipulation, require a priori mode schedules or are too computationally complex to run at real-time rates. We present a method based on the alternating direction method of multipliers (ADMM) that is capable of high-speed reasoning over potential contact events. Via a consensus formulation, our approach enables parallelization of the contact scheduling problem. We validate our results on five numerical examples, including four high-dimensional frictional contact problems, and a physical experimentation on an underactuated multi-contact system. We further demonstrate the effectiveness of our method on a physical experiment accomplishing a high-dimensional, multi-contact manipulation task with a robot arm.

Particle-based fluid simulations have emerged as a powerful tool for solving the Navier-Stokes equations, especially in cases that include intricate physics and free surfaces. The recent addition of machine learning methods to the toolbox for solving such problems is pushing the boundary of the quality vs. speed tradeoff of such numerical simulations. In this work, we lead the way to Lagrangian fluid simulators compatible with deep learning frameworks, and propose JAX-SPH - a Smoothed Particle Hydrodynamics (SPH) framework implemented in JAX. JAX-SPH builds on the code for dataset generation from the LagrangeBench project (Toshev et al., 2023) and extends this code in multiple ways: (a) integration of further key SPH algorithms, (b) restructuring the code toward a Python library, (c) verification of the gradients through the solver, and (d) demonstration of the utility of the gradients for solving inverse problems as well as a Solver-in-the-Loop application. Our code is available at //github.com/tumaer/jax-sph.

Causal inference is a fundamental research topic for discovering the cause-effect relationships in many disciplines. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to identify linear relationships, while others are applicable for non-linearities. Algorithms further vary in their sensitivity to noise and their ability to infer causal information from coupled vs. non-coupled time series. Therefore, different algorithms often generate different causal relationships for the same input. To achieve a more robust causal inference result, this publication proposes a novel data-driven two-phase multi-split causal ensemble model to combine the strengths of different causality base algorithms. In comparison to existing approaches, the proposed ensemble method reduces the influence of noise through a data partitioning scheme in the first phase. To achieve this, the data are initially divided into several partitions and the base algorithms are applied to each partition. Subsequently, Gaussian mixture models are used to identify the causal relationships derived from the different partitions that are likely to be valid. In the second phase, the identified relationships from each base algorithm are then merged based on three combination rules. The proposed ensemble approach is evaluated using multiple metrics, among them a newly developed evaluation index for causal ensemble approaches. We perform experiments using three synthetic datasets with different volumes and complexity, which are specifically designed to test causality detection methods under different circumstances while knowing the ground truth causal relationships. In these experiments, our causality ensemble outperforms each of its base algorithms. In practical applications, the use of the proposed method could hence lead to more robust and reliable causality results.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.