用于优化高斯混合策略的Wasserstein梯度流
Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policies
AI总结：
提出将基于GMMs的机器人策略优化转化为Wasserstein梯度流问题，利用$L^2$-Wasserstein距离和Bures-Wasserstein流形约束更新，在避障等任务中提升了成功率与稳定性。
摘要：
机器人通常依赖一系列预先学习的运动策略来执行复杂多样的任务。当面临未见过的任务条件或出现新任务需求时，机器人必须相应地调整其运动策略。在此背景下，策略优化是作为特定任务目标的函数来调整机器人策略的事实上的范式。最常用的运动策略具有特定的结构，而这些结构在策略优化算法中常被忽视。我们则提出利用概率策略的结构，将策略优化转化为最优传输问题。具体而言，我们专注于基于高斯混合模型（GMMs）构建的机器人运动策略，并将策略优化表述为GMMs空间上的Wasserstein梯度流。这自然允许我们通过GMMs之间的$L^2$-Wasserstein距离来约束策略更新，以增强策略优化过程的稳定性。此外，我们利用Bures-Wasserstein流形的几何特性，通过黎曼优化来优化GMM策略的高斯分布。我们在常见机器人设置上评估了该方法：到达运动、避障行为和多目标任务。结果表明，在任务成功率和低方差解决方案方面，我们的方法优于常见的策略优化基线。
英文摘要：
Robots often rely on a repertoire of previously-learned motion policies for performing tasks of diverse complexities. When facing unseen task conditions or when new task requirements arise, robots must adapt their motion policies accordingly. In this context, policy optimization is the \emph{de facto} paradigm to adapt robot policies as a function of task-specific objectives. Most commonly-used motion policies carry particular structures that are often overlooked in policy optimization algorithms. We instead propose to leverage the structure of probabilistic policies by casting the policy optimization as an optimal transport problem. Specifically, we focus on robot motion policies that build on Gaussian mixture models (GMMs) and formulate the policy optimization as a Wassertein gradient flow over the GMMs space. This naturally allows us to constrain the policy updates via the $L^2$-Wasserstein distance between GMMs to enhance the stability of the policy optimization process. Furthermore, we leverage the geometry of the Bures-Wasserstein manifold to optimize the Gaussian distributions of the GMM policy via Riemannian optimization. We evaluate our approach on common robotic settings: Reaching motions, collision-avoidance behaviors, and multi-goal tasks. Our results show that our method outperforms common policy optimization baselines in terms of task success rate and low-variance solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
