To do so, our input trajectories are parametrized in consecutive sections, e.g. as consecutive piecewise ramps or splines.

In this paper, we first propose a flexible framework for safe screening based on the Fenchel-Rockafellar duality and then deriveastrong safe screening rule for norm-regularized least squares using the proposed framework.

In reinforcement learning, continuous time is often discretized by a time scale δ, to which the resulting performance is known to be highly sensitive. In this work, we seek tofind aδ-invariantalgorithm for policygradient (PG) methods, which performs well regardless of the value ofδ. We first identify the underlying reasons that cause PG methods to fail asδ 0, proving that the variance of the PG estimator can diverge to infinity in stochastic environments under a certain assumption of stochasticity. While durative actions or action repetition can be employed to haveδ-invariance, previous action repetition methods cannot immediately react to unexpected situations in stochastic environments. We thus propose a novelδ-invariant method namedSafe Action Repetition (SAR) applicable to any existing PG algorithm. SAR can handle the stochasticity of environments byadaptivelyreacting tochanges instates during action repetition.

For statistical learning in high dimension, sparse regularizations have proven useful to boost both computational and statistical efficiency.

For time-series modeling we employ a Gaussian process with a nonlinear exogenous input structure.

Abstract--Legged robots can sense terrain through force interactions during locomotion, offering more reliable traversability estimates than remote sensing and serving as scouts for guiding wheeled rovers in challenging environments. However, even legged scouts face challenges when traversing highly deformable or unstable terrain. We present Safe Active Exploration for Granular T errain (SAEGT), a navigation framework that enables legged robots to safely explore unknown granular environments using proprioceptive sensing, particularly where visual input fails to capture terrain deformability. SAEGT estimates the safe region and frontier region online from leg-terrain interactions using Gaussian Process regression for traversability assessment, with a reactive controller for real-time safe exploration and navigation. SAEGT demonstrated its ability to safely explore and navigate toward a specified goal using only proprioceptively estimated traversability in simulation.

As will be shown in Section 4.1,