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We address multi-robot geometric task-and-motion planning (MR-GTAMP) problems in synchronous, monotone setups. The goal of the MR-GTAMP problem is to move objects with multiple robots to goal regions in the presence of other movable objects. We focus on collaborative manipulation tasks where the robots have to adopt intelligent collaboration strategies to be successful and effective, i.e., decide which robot should move which objects to which positions, and perform collaborative actions, such as handovers. To endow robots with these collaboration capabilities, we propose to first collect occlusion and reachability information for each robot by calling motion-planning algorithms. We then propose a method that uses the collected information to build a graph structure which captures the precedence of the manipulations of different objects and supports the implementation of a mixed-integer program to guide the search for highly effective collaborative task-and-motion plans. The search process for collaborative task-and-motion plans is based on a Monte-Carlo Tree Search (MCTS) exploration strategy to achieve exploration-exploitation balance. We evaluate our framework in two challenging MR-GTAMP domains and show that it outperforms two state-of-the-art baselines with respect to the planning time, the resulting plan length and the number of objects moved. We also show that our framework can be applied to underground mining operations where a robotic arm needs to coordinate with an autonomous roof bolter. We demonstrate plan execution in two roof-bolting scenarios both in simulation and on robots.

We present a new algorithm, Cross-Episodic Curriculum (CEC), to boost the learning efficiency and generalization of Transformer agents. Central to CEC is the placement of cross-episodic experiences into a Transformer's context, which forms the basis of a curriculum. By sequentially structuring online learning trials and mixed-quality demonstrations, CEC constructs curricula that encapsulate learning progression and proficiency increase across episodes. Such synergy combined with the potent pattern recognition capabilities of Transformer models delivers a powerful cross-episodic attention mechanism. The effectiveness of CEC is demonstrated under two representative scenarios: one involving multi-task reinforcement learning with discrete control, such as in DeepMind Lab, where the curriculum captures the learning progression in both individual and progressively complex settings; and the other involving imitation learning with mixed-quality data for continuous control, as seen in RoboMimic, where the curriculum captures the improvement in demonstrators' expertise. In all instances, policies resulting from CEC exhibit superior performance and strong generalization. Code is open-sourced at //cec-agent.github.io/ to facilitate research on Transformer agent learning.

Sparse Candecomp / PARAFAC decomposition, a generalization of the matrix singular value decomposition to higher-dimensional tensors, is a popular tool for analyzing diverse datasets. On tensors with billions of nonzero entries, computing a CP decomposition is a computationally intensive task. We propose the first distributed-memory implementations of two randomized CP decomposition algorithms, CP-ARLS-LEV and STS-CP, that offer nearly an order-of-magnitude speedup at high decomposition ranks over well-tuned non-randomized decomposition packages. Both algorithms rely on leverage score sampling and enjoy strong theoretical guarantees, each with varying time and accuracy tradeoffs. We tailor the communication schedule for our random sampling algorithms, eliminating expensive reduction collectives and forcing communication costs to scale with the random sample count. Finally, we optimize the local storage format for our methods, switching between an analogue of compressed sparse column and compressed sparse row formats to facilitate both random sampling and efficient parallelization of sparse-dense matrix multiplication. Experiments show that our methods are fast and scalable, producing 11x speedup over SPLATT to compute a decomposition of the billion-scale Reddit tensor on 512 CPU cores in under 2 minutes.

We study the dynamic pricing problem where the demand function is nonparametric and H\"older smooth, and we focus on adaptivity to the unknown H\"older smoothness parameter $\beta$ of the demand function. Traditionally the optimal dynamic pricing algorithm heavily relies on the knowledge of $\beta$ to achieve a minimax optimal regret of $\widetilde{O}(T^{\frac{\beta+1}{2\beta+1}})$. However, we highlight the challenge of adaptivity in this dynamic pricing problem by proving that no pricing policy can adaptively achieve this minimax optimal regret without knowledge of $\beta$. Motivated by the impossibility result, we propose a self-similarity condition to enable adaptivity. Importantly, we show that the self-similarity condition does not compromise the problem's inherent complexity since it preserves the regret lower bound $\Omega(T^{\frac{\beta+1}{2\beta+1}})$. Furthermore, we develop a smoothness-adaptive dynamic pricing algorithm and theoretically prove that the algorithm achieves this minimax optimal regret bound without the prior knowledge $\beta$.

We develop a class of interacting particle systems for implementing a maximum marginal likelihood estimation (MMLE) procedure to estimate the parameters of a latent variable model. We achieve this by formulating a continuous-time interacting particle system which can be seen as a Langevin diffusion over an extended state space of parameters and latent variables. In particular, we prove that the parameter marginal of the stationary measure of this diffusion has the form of a Gibbs measure where number of particles acts as the inverse temperature parameter in classical settings for global optimisation. Using a particular rescaling, we then prove geometric ergodicity of this system and bound the discretisation error in a manner that is uniform in time and does not increase with the number of particles. The discretisation results in an algorithm, termed Interacting Particle Langevin Algorithm (IPLA) which can be used for MMLE. We further prove nonasymptotic bounds for the optimisation error of our estimator in terms of key parameters of the problem, and also extend this result to the case of stochastic gradients covering practical scenarios. We provide numerical experiments to illustrate the empirical behaviour of our algorithm in the context of logistic regression with verifiable assumptions. Our setting provides a straightforward way to implement a diffusion-based optimisation routine compared to more classical approaches such as the Expectation Maximisation (EM) algorithm, and allows for especially explicit nonasymptotic bounds.

Recently, Graph Transformer (GT) models have been widely used in the task of Molecular Property Prediction (MPP) due to their high reliability in characterizing the latent relationship among graph nodes (i.e., the atoms in a molecule). However, most existing GT-based methods usually explore the basic interactions between pairwise atoms, and thus they fail to consider the important interactions among critical motifs (e.g., functional groups consisted of several atoms) of molecules. As motifs in a molecule are significant patterns that are of great importance for determining molecular properties (e.g., toxicity and solubility), overlooking motif interactions inevitably hinders the effectiveness of MPP. To address this issue, we propose a novel Atom-Motif Contrastive Transformer (AMCT), which not only explores the atom-level interactions but also considers the motif-level interactions. Since the representations of atoms and motifs for a given molecule are actually two different views of the same instance, they are naturally aligned to generate the self-supervisory signals for model training. Meanwhile, the same motif can exist in different molecules, and hence we also employ the contrastive loss to maximize the representation agreement of identical motifs across different molecules. Finally, in order to clearly identify the motifs that are critical in deciding the properties of each molecule, we further construct a property-aware attention mechanism into our learning framework. Our proposed AMCT is extensively evaluated on seven popular benchmark datasets, and both quantitative and qualitative results firmly demonstrate its effectiveness when compared with the state-of-the-art methods.

We prove that any semi-streaming algorithm for $(1-\epsilon)$-approximation of maximum bipartite matching requires \[ \Omega(\frac{\log{(1/\epsilon)}}{{\log{(1/\beta)}}}) \] passes, where $\beta \in (0,1)$ is the largest parameter so that an $n$-vertex graph with $n^{\beta}$ edge-disjoint induced matchings of size $\Theta(n)$ exist (such graphs are referred to as RS graphs). Currently, it is known that \[ \Omega(\frac{1}{\log\log{n}}) \leqslant \beta \leqslant 1-\Theta(\frac{\log^*{n}}{{\log{n}}}) \] and closing this huge gap between upper and lower bounds has remained a notoriously difficult problem in combinatorics. Under the plausible hypothesis that $\beta = \Omega(1)$, our lower bound result provides the first pass-approximation lower bound for (small) constant approximation of matchings in the semi-streaming model, a longstanding open question in the graph streaming literature. Our techniques are based on analyzing communication protocols for compressing (hidden) permutations. Prior work in this context relied on reducing such problems to Boolean domain and analyzing them via tools like XOR Lemmas and Fourier analysis on Boolean hypercube. In contrast, our main technical contribution is a hardness amplification result for permutations through concatenation in place of prior XOR Lemmas. This result is proven by analyzing permutations directly via simple tools from group representation theory combined with detailed information-theoretic arguments, and can be of independent interest.

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.

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.