Michael Ziegltrum, Jianhao Jiao, Tianhu Peng, Chengxu Zhou, Dimitrios Kanoulas
原文摘要
Agile locomotion is important for quadruped robots in the real world. Recent approaches have demonstrated impressive capabilities including dynamic climbing and jumping but typically rely on sequential multilayer perceptron (MLP) architectures with densely activated layers. In contrast, sparsely gated mixture-of-experts (MoE) architectures have become popular in the large language model (LLM) domain as a tool to improving scalability and performance by activating only a subset of parameters at inference. In this work, we investigate the application of such architectures to vision-based robotic locomotion. We compare policies based on standard MLPs and MoE architectures under a controlled setting where the number of active parameters at inference time is matched. Experimental results show an 8\% increase in reward during training comparing the MoE to a standard MLP and even show benefits comparing to MLPs with equivalent total parameters. Experimental results on a real Unitree Go2 quadruped robot demonstrate performance in the real world. These results highlight that sparsely gated MoE architectures may pose advantages in tasks where network capacity is important and that borrowing techniques from the fast-moving LLM space and applying them to locomotion is a promising direction.
We study how well approximation guarantees for clustering under one norm translate into guarantees under another. Specifically, we compare $k$-clustering in $\mathbb{R}^d$ under the $L_1$ and $L_2$ objectives, defined as the sums of Manhattan and Euclidean distances, respectively. In the worst case, the elementary relationship between these norms yields a $\sqrt{d}$ approximation bound, which is already tight for $k=2$. We therefore investigate whether stronger guarantees are possible in a natural average-case model, where the dataset is arbitrary but the coordinate system is chosen uniformly at random among all orthonormal bases. Our main result shows that, when $d=Ω(\log k)$, with high probability over the random rotation, any $β$-approximate $L_1$ clustering, with optimally chosen centers for its clusters, is also an $O(β)$-approximation under the $L_2$ objective. We also establish an expected approximation ratio of $O(β\min\{\sqrt{d},k^{2/d}\})$, yielding a dimension-independent bound of $O(β\sqrt{\log k/\log\log k})$. We obtain analogous guarantees in the reverse direction, from $L_2$ to $L_1$. We complement these results with lower bounds of $Ω(\min\{\sqrt{d},k^{1/d}\})$ in both directions, showing that our dimension-independent guarantees have asymptotically optimal dependence on $k$ for constant $β$. Our proofs overcome the dependence of the algorithm's output on the random rotation using geometric projection arguments and small Euclidean coresets. In particular, our results provide guarantees for existing clustering algorithms without requiring their redesign.
We study deterministic strategyproof mechanisms for facility location in finite-dimensional Euclidean spaces. For every population of at least three agents and every finite dimension, the coordinate-wise median minimizes the worst-case approximation ratio among anonymous mechanisms. Agent identities can improve the ratio at a fixed population size, and we give an explicit four-agent separation. Nevertheless, for every fixed dimension, the optimal ratio over all deterministic strategyproof mechanisms converges, as the population grows, to the supremum of the median's ratios over finite populations. Combined with the sharp bound for the median, this gives the optimal guarantee $\sqrt{6\sqrt3-8}$ uniform over populations and dimensions. The main structural ingredient is a rigidity theorem for strategyproof aggregation. We characterize unanimous, anonymous, translation-equivariant strategyproof mechanisms with bounded individual influence as fixed coordinate-wise order-statistic rules in a single orthonormal frame. We also prove that, for strategyproof mechanisms, continuity is equivalent to convexity of the full range in every finite dimension. An approximation-preserving normalization and a reflection argument yield the fixed-population anonymous comparison. To remove anonymity in the large-population limit, we develop an extraction theorem that converts a common guarantee on arbitrarily large populations into an anonymous deterministic mechanism on any prescribed finite population.