arXiv subjects

Shivam Vats

Publications and source records attributed to Shivam Vats.

18 recordsLinked to original sources

arXiv2026

Deliberate Practice: Learning Robot Skills under a Budget

We consider the problem of autonomously learning robot skills under a limited practice budget for sequential tasks. We propose an active skill learning algorithm, \emph{Deliberate Practice (DP)}, that computes a provably \emph{budget-optimal} allocation---practicing skills that maximize expected cumulative reward while being learnable within the budget. DP estimates both the time needed to master skills and the cumulative reward of the task plans that the skills unlock. Computing a budget-optimal allocation is challenging as it requires reasoning about combinatorially many skill plans over a large practice budget. Our key contribution is a bilinear program that can compute this exactly using off-the-shelf solvers. Through simulated and real-world experiments on long-horizon manipulation tasks, we show that our approach allows robots to optimally use limited practice time to acquire useful policies and improve long-horizon planning.

cs.RO↗

arXiv2026

Positive Cones of Parabolic Grassmann Bundle over a curve

In this article, we define the parabolic Grassmann bundle associated to a parabolic vector bundle over a smooth projective variety, generalizing the construction of parabolic projective bundles developed in \cite{BL}. We determine its N\'eron--Severi group and compute its nef, pseudoeffective, and Mori cones over smooth projective curves. We also compute the corresponding cones for the fiber product of two parabolic Grassmann bundles over a smooth projective curve.

math.AG↗

arXiv2026

When Life Gives You BC, Make Q-functions: Extracting Q-values from Behavior Cloning for On-Robot Reinforcement Learning

Behavior Cloning (BC) has emerged as a highly effective paradigm for robot learning. However, BC lacks a self-guided mechanism for online improvement after demonstrations have been collected. Existing offline-to-online learning methods often cause policies to replace previously learned good actions due to a distribution mismatch between offline data and online learning. In this work, we propose Q2RL, Q-Estimation and Q-Gating from BC for Reinforcement Learning, an algorithm for efficient offline-to-online learning. Our method consists of two parts: (1) Q-Estimation extracts a Q-function from a BC policy using a few interaction steps with the environment, followed by online RL with (2) Q-Gating, which switches between BC and RL policy actions based on their respective Q-values to collect samples for RL policy training. Across manipulation tasks from D4RL and robomimic benchmarks, Q2RL outperforms SOTA offline-to-online learning baselines on success rate and time to convergence. Q2RL is efficient enough to be applied in an on-robot RL setting, learning robust policies for contact-rich and high precision manipulation tasks such as pipe assembly and kitting, in 1-2 hours of online interaction, achieving success rates of up to 100% and up to 3.75x improvement against the original BC policy. Code and video are available at https://pages.rai-inst.com/q2rl_website/

cs.RO↗

arXiv2026

Creative Robot Tool Use by Counterfactual Reasoning

We propose a causal reasoning framework for creative robot tool use where a suitable tool for a task is correctly identified for use beyond its primary objectives. The proposed framework first discovers the causal relationships between the tool and the task by conducting simulated experiments in a dynamics model. We decouple the causal discovery problem into two complementary components: VLM-based feature suggestion and counterfactual tool generation via targeted geometric and physical feature perturbations. Then, novel objects are classified based on identified causal features, and the tool use skill is transferred via keypoint matching conditioned on the identified causal features. By reconstructing the task in a dynamics model, our approach grounds tool use in the physics of the problem. We illustrate our approach in reaching a distant object with different sticks, scooping candies from a bowl using diverse items, and using different boxes or crates as stepping platforms to retrieve an object from a high shelf. Our baseline comparisons show that identifying causal features and grounding them in physical tool properties leads to more reliable tool selection and stronger skill keypoint transfer.

cs.RO↗

arXiv2026

Singularity of cubic hypersurfaces and hyperplane sections of projectivized tangent bundle of projective space

We show that the normal points of a cubic hypersurface in projective space have canonical singularities unless the hypersurface is an iterated cone over an elliptic curve. As an application, we give a simple linear algebraic description of all the hyperplane sections of projectivized tangent bundle of projective space, hence describing hyperplane sections of a rational homogeneous manifold of Picard rank $2$. This also simplifies and extends recent results of Mazouni-Nagaraj in higher dimensions. We also compute the Chow ring of these hyperplane sections.

math.AG↗

arXiv2025

Automorphisms of punctual Hilbert schemes and symmetric powers of varieties

We classify complex smooth projective surfaces whose punctual Hilbert scheme has a non-natural automorphism preserving the big diagonal. This completely answers a question raised by Belmans, Oberdieck and Rennemo, and extends previous works by Boissi{è}re-Sarti, Hayashi, Sasaki, Girardet and Wang. We reduce this to studying the existence of non-natural automorphisms of symmetric powers. We study this question for higher dimensional varieties too, giving some sufficient conditions guaranteeing every automorphism of a symmetric power to be natural. As a corollary, we characterize smooth projective surfaces of Kodaira dimension $\geq 1$ whose punctual Hilbert scheme has a non-natural automorphism, this time not assuming the automorphism preserves the big diagonal. We also address the question, when a smooth projective variety is determined up to isomorphism by its punctual Hilbert scheme.

math.AG↗

arXiv2025

Isomorphisms and automorphisms of multiprojective bundles and symmetric powers of projective bundles

We describe when two multiprojective bundles (fibre products of projective bundles over the same base) over projective spaces are isomorphic as abstract varieties. We also describe when two relative symmetric powers of projective bundles over projective spaces are isomorphic. Finally, we describe the automorphisms of multiprojective bundles and relative symmetric powers of projective bundles over projective spaces.

math.AG↗

arXiv2025

Symmetric power of higher dimensional varieties

We study several properties of the symmetric power $S^mX$ of a smooth variety $X$. We describe the Picard and divisor class groups of $S^mX$ when $X$ is projective. We give a complete description of the stratification of $S^mX$ by iterated singular locus in terms of some combinatorial data regarding partitions of the integer $m.$ This gives a new viewpoint of a natural stratification of $S^mX$ by multiplicities.

math.AG↗

arXiv2025

Accelerating Residual Reinforcement Learning with Uncertainty Estimation

Residual Reinforcement Learning (RL) is a popular approach for adapting pretrained policies by learning a lightweight residual policy that provides corrective actions. While Residual RL is more sample-efficient than finetuning the entire base policy, existing methods struggle with sparse rewards and are designed for deterministic base policies. We propose two improvements to Residual RL that further enhance its sample efficiency and make it suitable for stochastic base policies. First, we leverage uncertainty estimates of the base policy to focus exploration on regions in which the base policy is not confident. Second, we propose a simple modification to off-policy residual learning that allows it to observe base actions and better handle stochastic base policies. We evaluate our method with both Gaussian-based and Diffusion-based stochastic base policies on tasks from Robosuite and D4RL, and compare against state-of-the-art finetuning methods, demo-augmented RL methods, and other residual RL methods. Our algorithm significantly outperforms existing baselines in a variety of simulation benchmark environments. We also deploy our learned polices in the real world to demonstrate their robustness with zero-shot sim-to-real transfer. Paper homepage : lakshitadodeja.github.io/uncertainty-aware-residual-rl/

cs.LG↗

arXiv2025

Multi-Robot Motion Planning with Diffusion Models

Diffusion models have recently been successfully applied to a wide range of robotics applications for learning complex multi-modal behaviors from data. However, prior works have mostly been confined to single-robot and small-scale environments due to the high sample complexity of learning multi-robot diffusion models. In this paper, we propose a method for generating collision-free multi-robot trajectories that conform to underlying data distributions while using only single-robot data. Our algorithm, Multi-robot Multi-model planning Diffusion (MMD), does so by combining learned diffusion models with classical search-based techniques -- generating data-driven motions under collision constraints. Scaling further, we show how to compose multiple diffusion models to plan in large environments where a single diffusion model fails to generalize well. We demonstrate the effectiveness of our approach in planning for dozens of robots in a variety of simulated scenarios motivated by logistics environments. View video demonstrations and code at: https://multi-robot-diffusion.github.io/.

cs.RO↗

arXiv2025

Optimal Interactive Learning on the Job via Facility Location Planning

Collaborative robots must continually adapt to novel tasks and user preferences without overburdening the user. While prior interactive robot learning methods aim to reduce human effort, they are typically limited to single-task scenarios and are not well-suited for sustained, multi-task collaboration. We propose COIL (Cost-Optimal Interactive Learning) -- a multi-task interaction planner that minimizes human effort across a sequence of tasks by strategically selecting among three query types (skill, preference, and help). When user preferences are known, we formulate COIL as an uncapacitated facility location (UFL) problem, which enables bounded-suboptimal planning in polynomial time using off-the-shelf approximation algorithms. We extend our formulation to handle uncertainty in user preferences by incorporating one-step belief space planning, which uses these approximation algorithms as subroutines to maintain polynomial-time performance. Simulated and physical experiments on manipulation tasks show that our framework significantly reduces the amount of work allocated to the human while maintaining successful task completion.

cs.RO↗

arXiv2025

RecoveryChaining: Learning Local Recovery Policies for Robust Manipulation

Model-based planners and controllers are commonly used to solve complex manipulation problems as they can efficiently optimize diverse objectives and generalize to long horizon tasks. However, they often fail during deployment due to noisy actuation, partial observability and imperfect models. To enable a robot to recover from such failures, we propose to use hierarchical reinforcement learning to learn a recovery policy. The recovery policy is triggered when a failure is detected based on sensory observations and seeks to take the robot to a state from which it can complete the task using the nominal model-based controllers. Our approach, called RecoveryChaining, uses a hybrid action space, where the model-based controllers are provided as additional \emph{nominal} options which allows the recovery policy to decide how to recover, when to switch to a nominal controller and which controller to switch to even with \emph{sparse rewards}. We evaluate our approach in three multi-step manipulation tasks with sparse rewards, where it learns significantly more robust recovery policies than those learned by baselines. We successfully transfer recovery policies learned in simulation to a physical robot to demonstrate the feasibility of sim-to-real transfer with our method.

cs.RO↗

arXiv2024

Extremal Contraction of Projective Bundles

In this article, we explore the extremal contractions of several projective bundles over smooth Fano varieties of Picard rank $1$. We provide a whole class of examples of projective bundles with smooth blow-up structures, derived from the notion of drums which was introduced by Occhetta-Romano-Conde-Wiśniewski to study interaction with $\mathbb{C}^*$-actions and birational geometry. By manipulating projective bundles, we give a simple geometric construction of the rooftop flip, which was introduced recently by Barban-Franceschini. Additionally, we obtain analogues of some recent results of Vats in higher dimensions. The list of projective bundles we consider includes all globally generated bundles over projective space with first Chern class $2$. For each of them, we compute the nef and pseudoeffective cones.

math.AG↗

arXiv2023

Correspondence between Projective bundles over $\mathbb{P}^{2}$ and rational Hypersurfaces in $\mathbb{P}^{4}$

Let E be the restriction of the null-correlation bundle on $\mathbb{P}^{3}$ to a hyperplane. In this article, we show that the projective bundle $\mathbb{P}(E)$ is isomorphic to a blow-up of a non-singular quadric in $\mathbb{P}^{4}$ along a line. We also prove that for each $d \geq 2$, there are hypersurfaces of degree d containing a line in $\mathbb{P}^{4}$ whose blow-up along the line is isomorphic to the projective bundle over $\mathbb{P}^{2}$.

math.AG↗

arXiv2023

Isomorphism of Multiprojective Bundles and Projective Towers

We study when two projective bundles over two arbitrary smooth projective varieties of different dimensions can be isomorphic. We show that two multi-projective bundles (fibre product of projective bundles) over different projective spaces cannot be isomorphic, except in the trivial case. We also give necessary and sufficient conditions for the top varieties of two height 3 towers of projective bundles being isomorphic, under certain assumptions.

math.AG↗

arXiv2023

Efficient Recovery Learning using Model Predictive Meta-Reasoning

Operating under real world conditions is challenging due to the possibility of a wide range of failures induced by execution errors and state uncertainty. In relatively benign settings, such failures can be overcome by retrying or executing one of a small number of hand-engineered recovery strategies. By contrast, contact-rich sequential manipulation tasks, like opening doors and assembling furniture, are not amenable to exhaustive hand-engineering. To address this issue, we present a general approach for robustifying manipulation strategies in a sample-efficient manner. Our approach incrementally improves robustness by first discovering the failure modes of the current strategy via exploration in simulation and then learning additional recovery skills to handle these failures. To ensure efficient learning, we propose an online algorithm called Meta-Reasoning for Skill Learning (MetaReSkill) that monitors the progress of all recovery policies during training and allocates training resources to recoveries that are likely to improve the task performance the most. We use our approach to learn recovery skills for door-opening and evaluate them both in simulation and on a real robot with little fine-tuning. Compared to open-loop execution, our experiments show that even a limited amount of recovery learning improves task success substantially from 71% to 92.4% in simulation and from 75% to 90% on a real robot.

cs.RO↗

arXiv2022

Synergistic Scheduling of Learning and Allocation of Tasks in Human-Robot Teams

We consider the problem of completing a set of $n$ tasks with a human-robot team using minimum effort. In many domains, teaching a robot to be fully autonomous can be counterproductive if there are finitely many tasks to be done. Rather, the optimal strategy is to weigh the cost of teaching a robot and its benefit -- how many new tasks it allows the robot to solve autonomously. We formulate this as a planning problem where the goal is to decide what tasks the robot should do autonomously (act), what tasks should be delegated to a human (delegate) and what tasks the robot should be taught (learn) so as to complete all the given tasks with minimum effort. This planning problem results in a search tree that grows exponentially with $n$ -- making standard graph search algorithms intractable. We address this by converting the problem into a mixed integer program that can be solved efficiently using off-the-shelf solvers with bounds on solution quality. To predict the benefit of learning, we propose a precondition prediction classifier. Given two tasks, this classifier predicts whether a skill trained on one will transfer to the other. Finally, we evaluate our approach on peg insertion and Lego stacking tasks, both in simulation and real-world, showing substantial savings in human effort.

cs.RO↗

arXiv2022

Search-Based Task Planning with Learned Skill Effect Models for Lifelong Robotic Manipulation

Robots deployed in many real-world settings need to be able to acquire new skills and solve new tasks over time. Prior works on planning with skills often make assumptions on the structure of skills and tasks, such as subgoal skills, shared skill implementations, or task-specific plan skeletons, which limit adaptation to new skills and tasks. By contrast, we propose doing task planning by jointly searching in the space of parameterized skills using high-level skill effect models learned in simulation. We use an iterative training procedure to efficiently generate relevant data to train such models. Our approach allows flexible skill parameterizations and task specifications to facilitate lifelong learning in general-purpose domains. Experiments demonstrate the ability of our planner to integrate new skills in a lifelong manner, finding new task strategies with lower costs in both train and test tasks. We additionally show that our method can transfer to the real world without further fine-tuning.

cs.RO↗