Viraj Joshi | Searcharxiv

arXiv2026

From Bowditch question to Goldman conjecture for type-preserving representations

For punctured surfaces $\Sigma_{g,p}$ of genus $g\geqslant 2$, we explore the dynamics of the mapping class group action on the relative $\mathrm{PSL}(2,\mathbb{R})$-character varieties of type-preserving representations. For such relative character varieties, Goldman's conjecture predicts that the mapping class group acts ergodically on their non-Teichm\"uller components. A related question of Bowditch asks whether every non-elementary type-preserving representation that is non-Fuchsian sends some non-peripheral simple closed curve to a non-hyperbolic element. We show that, on the components of the relative character variety indexed by fixed signs of images of peripheral elements and relative Euler classes non-extremal in the generalized Milnor-Wood inequality, an affirmative answer to Bowditch's question implies Goldman's conjecture.

math.GT↗

arXiv2025

Benchmarking Massively Parallelized Multi-Task Reinforcement Learning for Robotics Tasks

Multi-task Reinforcement Learning (MTRL) has emerged as a critical training paradigm for applying reinforcement learning (RL) to a set of complex real-world robotic tasks, which demands a generalizable and robust policy. At the same time, \emph{massively parallelized training} has gained popularity, not only for significantly accelerating data collection through GPU-accelerated simulation but also for enabling diverse data collection across multiple tasks by simulating heterogeneous scenes in parallel. However, existing MTRL research has largely been limited to off-policy methods like SAC in the low-parallelization regime. MTRL could capitalize on the higher asymptotic performance of on-policy algorithms, whose batches require data from the current policy, and as a result, take advantage of massive parallelization offered by GPU-accelerated simulation. To bridge this gap, we introduce a massively parallelized $\textbf{M}$ulti-$\textbf{T}$ask $\textbf{Bench}$mark for robotics (MTBench), an open-sourced benchmark featuring a broad distribution of 50 manipulation tasks and 20 locomotion tasks, implemented using the GPU-accelerated simulator IsaacGym. MTBench also includes four base RL algorithms combined with seven state-of-the-art MTRL algorithms and architectures, providing a unified framework for evaluating their performance. Our extensive experiments highlight the superior speed of evaluating MTRL approaches using MTBench, while also uncovering unique challenges that arise from combining massive parallelism with MTRL. Code is available at https://github.com/Viraj-Joshi/MTBench

cs.RO↗