Shankar Sastry

Mo Chen, Jaime F. Fisac, Shankar Sastry et al.

We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically, especially given the growing interest in utilizing unmanned aircraft systems for civil purposes. The direct solution of this problem by solving a single-obstacle Hamilton-Jacobi-Isaacs (HJI) variational inequality (VI) is numerically intractable due to the exponential scaling of computation complexity with problem dimensionality. Furthermore, the single-obstacle HJI VI cannot directly handle situations in which vehicles do not have a common scheduled arrival time. Instead, we perform sequential path planning by considering vehicles in order of priority, modeling higher-priority vehicles as time-varying obstacles for lower-priority vehicles. To do this, we solve a double-obstacle HJI VI which allows us to obtain the reach-avoid set, defined as the set of states from which a vehicle can reach its target while staying within a time-varying state constraint set. From the solution of the double-obstacle HJI VI, we can also extract the latest start time and the optimal control for each vehicle. This is a first application of the double-obstacle HJI VI which can handle systems with time-varying dynamics, target sets, and state constraint sets, and results in computation complexity that scales linearly, as opposed to exponentially, with the number of vehicles in consideration.

Deepan Muthirayan, Chinmay Maheshwari, Pramod P. Khargonekar et al.

We study the problem of online learning in two-sided non-stationary matching markets, where the objective is to converge to a stable match. In particular, we consider the setting where one side of the market, the arms, has fixed known set of preferences over the other side, the players. While this problem has been studied when the players have fixed but unknown preferences, in this work we study the problem of how to learn when the preferences of the players are time varying and unknown. Our contribution is a methodology that can handle any type of preference structure and variation scenario. We show that, with the proposed algorithm, each player receives a uniform sub-linear regret of {$\widetilde{\mathcal{O}}(L^{1/2}_TT^{1/2})$} up to the number of changes in the underlying preferences of the agents, $L_T$. Therefore, we show that the optimal rates for single-agent learning can be achieved in spite of the competition up to a difference of a constant factor. We also discuss extensions of this algorithm to the case where the number of changes need not be known a priori.

Chih-Yuan Chiu, Kshitij Kulkarni, Shankar Sastry

Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal discovery are often unable to uncover causal links, between random variables in a dynamic setting, that manifest only when the variables first experience low-probability realizations. To address this issue, we introduce a novel statistical independence test on data collected from time-invariant dynamical systems in which rare but consequential events occur. In particular, we exploit the time-invariance of the underlying data to construct a superimposed dataset of the system state before rare events happen at different timesteps. We then design a conditional independence test on the reorganized data. We provide non-asymptotic sample complexity bounds for the consistency of our method, and validate its performance across various simulated and real-world datasets, including incident data collected from the Caltrans Performance Measurement System (PeMS). Code containing the datasets and experiments is publicly available.

Chinmay Maheshwari, Manxi Wu, Druv Pai et al.

We study a multi-agent reinforcement learning dynamics, and analyze its asymptotic behavior in infinite-horizon discounted Markov potential games. We focus on the independent and decentralized setting, where players do not know the game parameters, and cannot communicate or coordinate. In each stage, players update their estimate of Q-function that evaluates their total contingent payoff based on the realized one-stage reward in an asynchronous manner. Then, players independently update their policies by incorporating an optimal one-stage deviation strategy based on the estimated Q-function. Inspired by the actor-critic algorithm in single-agent reinforcement learning, a key feature of our learning dynamics is that agents update their Q-function estimates at a faster timescale than the policies. Leveraging tools from two-timescale asynchronous stochastic approximation theory, we characterize the convergent set of learning dynamics.

Chinmay Maheshwari, Eric Mazumdar, Shankar Sastry

We study the problem of online learning in competitive settings in the context of two-sided matching markets. In particular, one side of the market, the agents, must learn about their preferences over the other side, the firms, through repeated interaction while competing with other agents for successful matches. We propose a class of decentralized, communication- and coordination-free algorithms that agents can use to reach to their stable match in structured matching markets. In contrast to prior works, the proposed algorithms make decisions based solely on an agent's own history of play and requires no foreknowledge of the firms' preferences. Our algorithms are constructed by splitting up the statistical problem of learning one's preferences, from noisy observations, from the problem of competing for firms. We show that under realistic structural assumptions on the underlying preferences of the agents and firms, the proposed algorithms incur a regret which grows at most logarithmically in the time horizon. Our results show that, in the case of matching markets, competition need not drastically affect the performance of decentralized, communication and coordination free online learning algorithms.

Max Fu, Justin Yu, Karim El-Refai et al.

"Code-as-Policy" considers how executable code can complement data-intensive Vision-Language-Action (VLA) methods, yet their effectiveness as autonomous controllers for embodied manipulation remains underexplored. We present CaP-X, an open-access framework for systematically studying Code-as-Policy agents in robot manipulation. At its core is CaP-Gym, an interactive environment in which agents control robots by synthesizing and executing programs that compose perception and control primitives. Building on this foundation, CaP-Bench evaluates frontier language and vision-language models across varying levels of abstraction, interaction, and perceptual grounding. Across 12 models, CaP-Bench reveals a consistent trend: performance improves with human-crafted abstractions but degrades as these priors are removed, exposing a dependence on designer scaffolding. At the same time, we observe that this gap can be mitigated through scaling agentic test-time computation--through multi-turn interaction, structured execution feedback, visual differencing, automatic skill synthesis, and ensembled reasoning--substantially improves robustness even when agents operate over low-level primitives. These findings allow us to derive CaP-Agent0, a training-free framework that recovers human-level reliability on several manipulation tasks in simulation and on real embodiments. We further introduce CaP-RL, showing reinforcement learning with verifiable rewards improves success rates and transfers from sim2real with minimal gap. Together, CaP-X provides a principled, open-access platform for advancing embodied coding agents.

Nima Rahmanian, Daniel Kienzle, Thomas Gossard et al.

We present TT4D, a large-scale, high-fidelity table tennis dataset. It provides $140+$ hours of reconstructed singles and doubles gameplay from monocular broadcast videos, featuring multimodal annotations like high-quality camera calibrations, precise 3D ball positions, ball spin, time segmentation, and 3D human meshes over time. This rich data provides a new foundation for virtual replay, in-depth player analysis, and robot learning. The dataset's combination of scale and precision is achieved through a novel reconstruction pipeline. Prior methods first partition a game sequence into individual shot segments based on the 2D ball track, and only then attempt reconstruction. However, 2D-based time segmentation collapses under occlusion and varied camera viewpoints, preventing reliable reconstruction. We invert this paradigm by first lifting the entire unsegmented 2D ball track to 3D through a learned lifting network. This 3D trajectory then allows us to reliably perform time segmentation. The learned lifting network also infers the ball's spin, handles unreliable ball detections, and successfully reconstructs the ball trajectory in cases of high occlusion. This lift-first design is necessary, as our pipeline is the only method capable of reconstructing table tennis gameplay from general-view broadcast monocular videos. We demonstrate the dataset's fidelity through two downstream tasks: estimating the racket's pose \& velocity at impact, and training a generative model of competitive rallies.

Chinmay Maheshwari, Manxi Wu, Shankar Sastry

Markov games provide a powerful framework for modeling strategic multi-agent interactions in dynamic environments. Traditionally, convergence properties of decentralized learning algorithms in these settings have been established only for special cases, such as Markov zero-sum and potential games, which do not fully capture real-world interactions. In this paper, we address this gap by studying the asymptotic properties of learning algorithms in general-sum Markov games. In particular, we focus on a decentralized algorithm where each agent adopts an actor-critic learning dynamic with asynchronous step sizes. This decentralized approach enables agents to operate independently, without requiring knowledge of others' strategies or payoffs. We introduce the concept of a Markov Near-Potential Function (MNPF) and demonstrate that it serves as an approximate Lyapunov function for the policy updates in the decentralized learning dynamics, which allows us to characterize the convergent set of strategies. We further strengthen our result under specific regularity conditions and with finite Nash equilibria.

Haoru Xue, Tairan He, Zi Wang et al.

Recent progress in GPU-accelerated, photorealistic simulation has opened a scalable data-generation path for robot learning, where massive physics and visual randomization allow policies to generalize beyond curated environments. Building on these advances, we develop a teacher-student-bootstrap learning framework for vision-based humanoid loco-manipulation, using articulated-object interaction as a representative high-difficulty benchmark. Our approach introduces a staged-reset exploration strategy that stabilizes long-horizon privileged-policy training, and a GRPO-based fine-tuning procedure that mitigates partial observability and improves closed-loop consistency in sim-to-real RL. Trained entirely on simulation data, the resulting policy achieves robust zero-shot performance across diverse door types and outperforms human teleoperators by up to 31.7% in task completion time under the same whole-body control stack. This represents the first humanoid sim-to-real policy capable of diverse articulated loco-manipulation using pure RGB perception.

Haoru Xue, Xiaoyu Huang, Dantong Niu et al.

Vision-language-action (VLA) models have demonstrated strong semantic understanding and zero-shot generalization, yet most existing systems assume an accurate low-level controller with hand-crafted action "vocabulary" such as end-effector pose or root velocity. This assumption confines prior work to quasi-static tasks and precludes the agile, whole-body behaviors required by humanoid whole-body control (WBC) tasks. To capture this gap in the literature, we start by introducing the first sim-to-real-ready, vision-language, closed-loop benchmark for humanoid WBC, comprising over 150 tasks from 10 categories. We then propose LeVERB: Latent Vision-Language-Encoded Robot Behavior, a hierarchical latent instruction-following framework for humanoid vision-language WBC, the first of its kind. At the top level, a vision-language policy learns a latent action vocabulary from synthetically rendered kinematic demonstrations; at the low level, a reinforcement-learned WBC policy consumes these latent verbs to generate dynamics-level commands. In our benchmark, LeVERB can zero-shot attain a 80% success rate on simple visual navigation tasks, and 58.5% success rate overall, outperforming naive hierarchical whole-body VLA implementation by 7.8 times.

Daniel Etaat, Dvij Kalaria, Nima Rahmanian et al.

Physical agility is a necessary skill in competitive table tennis, but by no means sufficient. Champions excel in this fast-paced and highly dynamic environment by anticipating their opponent's intent - buying themselves the necessary time to react. In this work, we take one step towards designing such an anticipatory agent. Previous works have developed systems capable of real-time table tennis gameplay, though they often do not leverage anticipation. Among the works that forecast opponent actions, their approaches are limited by dataset size and variety. Our paper contributes (1) a scalable system for reconstructing monocular video of table tennis matches in 3D and (2) an uncertainty-aware controller that anticipates opponent actions. We demonstrate in simulation that our policy improves the ball return rate against high-speed hits from 49.9% to 59.0% as compared to a baseline non-anticipatory policy.

Maria G. Mendoza, Victoria Marie Tuck, Chinmay Maheshwari et al.

A key challenge in disaster response is maintaining situational awareness of an evolving landscape, which requires balancing exploration of unobserved regions with sustained monitoring of changing Regions of Interest (ROIs). Unmanned Aerial Vehicles (UAVs) have emerged as an effective response tool, particularly in applications like environmental monitoring and search-and-rescue, due to their ability to provide aerial coverage, withstand hazardous conditions, and navigate quickly and flexibly. However, efficient and adaptable multi-robot coverage with limited sensing in disaster settings and evolving time-varying information maps remains a significant challenge, necessitating better methods for UAVs to continuously adapt their trajectories in response to changes. In this paper, we propose a decentralized multi-agent coverage framework that serves as a high-level planning strategy for adaptive coverage in unknown, time-varying environments under partial observability. Each agent computes an adaptive ergodic policy, implemented via a Markov-chain transition model, that tracks a continuously updated belief over the underlying importance map. Gaussian Processes are used to perform those online belief updates. The resulting policy drives agents to spend time in ROIs proportional to their estimated importance, while preserving sufficient exploration to detect and adapt to time-varying environmental changes. Unlike existing approaches that assume known importance maps, require centralized coordination, or assume a static environment, our framework addresses the combined challenges of unknown, time-varying distributions in a more realistic decentralized and partially observable setting. We compare against alternative coverage strategies and analyze our method's response to simulated disaster evolution, highlighting its improved adaptability and transient performance in dynamic scenarios.

Dvij Kalaria, Sudarshan S Harithas, Pushkal Katara et al.

We introduce DreamControl, a novel methodology for learning autonomous whole-body humanoid skills. DreamControl leverages the strengths of diffusion models and Reinforcement Learning (RL): our core innovation is the use of a diffusion prior trained on human motion data, which subsequently guides an RL policy in simulation to complete specific tasks of interest (e.g., opening a drawer or picking up an object). We demonstrate that this human motion-informed prior allows RL to discover solutions unattainable by direct RL, and that diffusion models inherently promote natural looking motions, aiding in sim-to-real transfer. We validate DreamControl's effectiveness on a Unitree G1 robot across a diverse set of challenging tasks involving simultaneous lower and upper body control and object interaction. Project website at https://genrobo.github.io/DreamControl/

Addison Kalanther, Sanika Bharvirkar, Shankar Sastry et al.

Multi-agent reinforcement learning (MARL) is increasingly used to design learning-enabled agents that interact in shared environments. However, training MARL algorithms in general-sum games remains challenging: learning dynamics can become unstable, and convergence guarantees typically hold only in restricted settings such as two-player zero-sum or fully cooperative games. Moreover, when agents have heterogeneous and potentially conflicting preferences, it is unclear what system-level objective should guide learning. In this paper, we propose a new MARL pipeline called Near-Potential Policy Optimization (NePPO) for computing approximate Nash equilibria in mixed cooperative--competitive environments. The core idea is to learn a player-independent potential function such that the Nash equilibrium of a cooperative game with this potential as the common utility approximates a Nash equilibrium of the original game. To this end, we introduce a novel MARL objective such that minimizing this objective yields the best possible potential function candidate and consequently an approximate Nash equilibrium of the original game. We develop an algorithmic pipeline that minimizes this objective using zeroth-order gradient descent and returns an approximate Nash equilibrium policy. We empirically show the superior performance of this approach compared to popular baselines such as MAPPO, IPPO and MADDPG.

Marsalis Gibson, David Babazadeh, Claire Tomlin et al.

Adversarial attacks on learning-based multi-modal trajectory predictors have already been demonstrated. However, there are still open questions about the effects of perturbations on inputs other than state histories, and how these attacks impact downstream planning and control. In this paper, we conduct a sensitivity analysis on two trajectory prediction models, Trajectron++ and AgentFormer. The analysis reveals that between all inputs, almost all of the perturbation sensitivities for both models lie only within the most recent position and velocity states. We additionally demonstrate that, despite dominant sensitivity on state history perturbations, an undetectable image map perturbation made with the Fast Gradient Sign Method can induce large prediction error increases in both models, revealing that these trajectory predictors are, in fact, susceptible to image-based attacks. Using an optimization-based planner and example perturbations crafted from sensitivity results, we show how these attacks can cause a vehicle to come to a sudden stop from moderate driving speeds.

Xin Guo, Xinyu Li, Chinmay Maheshwari et al.

We propose a new framework of Markov $α$-potential games to study Markov games. We show that any Markov game with finite-state and finite-action is a Markov $α$-potential game, and establish the existence of an associated $α$-potential function. Any optimizer of an $α$-potential function is shown to be an $α$-stationary Nash equilibrium. We study two important classes of practically significant Markov games, Markov congestion games and the perturbed Markov team games, via the framework of Markov $α$-potential games, with explicit characterization of an upper bound for $α$ and its relation to game parameters. Additionally, we provide a semi-infinite linear programming based formulation to obtain an upper bound for $α$ for any Markov game. Furthermore, we study two equilibrium approximation algorithms, namely the projected gradient-ascent algorithm and the sequential maximum improvement algorithm, along with their Nash regret analysis, and corroborate the results with numerical experiments.

Michael Psenka, Druv Pai, Vishal Raman et al.

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening Networks (FlatNet), are theoretically interpretable, computationally feasible at scale, and generalize well to test data, a balance not typically found in manifold-based learning methods. We present empirical results and comparisons to other models on synthetic high-dimensional manifold data and 2D image data. Our code is publicly available.

Kamil Nar, Shankar Sastry

While training error of most deep neural networks degrades as the depth of the network increases, residual networks appear to be an exception. We show that the main reason for this is the Lyapunov stability of the gradient descent algorithm: for an arbitrarily chosen step size, the equilibria of the gradient descent are most likely to remain stable for the parametrization of residual networks. We then present an architecture with a pair of residual networks to approximate a large class of functions by decomposing them into a convex and a concave part. Some parameters of this model are shown to change little during training, and this imperfect optimization prevents overfitting the data and leads to solutions with small Lipschitz constants, while providing clues about the generalization of other deep networks.

Joshua Achiam, Shankar Sastry

Exploration in complex domains is a key challenge in reinforcement learning, especially for tasks with very sparse rewards. Recent successes in deep reinforcement learning have been achieved mostly using simple heuristic exploration strategies such as $ε$-greedy action selection or Gaussian control noise, but there are many tasks where these methods are insufficient to make any learning progress. Here, we consider more complex heuristics: efficient and scalable exploration strategies that maximize a notion of an agent's surprise about its experiences via intrinsic motivation. We propose to learn a model of the MDP transition probabilities concurrently with the policy, and to form intrinsic rewards that approximate the KL-divergence of the true transition probabilities from the learned model. One of our approximations results in using surprisal as intrinsic motivation, while the other gives the $k$-step learning progress. We show that our incentives enable agents to succeed in a wide range of environments with high-dimensional state spaces and very sparse rewards, including continuous control tasks and games in the Atari RAM domain, outperforming several other heuristic exploration techniques.

Ehsan Elhamifar, Mahdi Soltanolkotabi, Shankar Sastry

High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover low-dimensional subspaces and address problems such as clustering, classification, subset selection and more. In this paper, we address the problem of recovering sparse representations for noisy data points in a dictionary whose columns correspond to corrupted data lying close to a union of subspaces. We consider a constrained $\ell_1$-minimization and study conditions under which the solution of the proposed optimization satisfies the approximate subspace-sparse recovery condition. More specifically, we show that each noisy data point, perturbed from a subspace by a noise of the magnitude of $\varepsilon$, will be reconstructed using data points from the same subspace with a small error of the order of $O(\varepsilon)$ and that the coefficients corresponding to data points in other subspaces will be sufficiently small, \ie, of the order of $O(\varepsilon)$. We do not impose any randomness assumption on the arrangement of subspaces or distribution of data points in each subspace. Our framework is based on a novel generalization of the null-space property to the setting where data lie in multiple subspaces, the number of data points in each subspace exceeds the dimension of the subspace, and all data points are corrupted by noise. Moreover, assuming a random distribution for data points, we further show that coefficients from the desired support not only reconstruct a given point with high accuracy, but also have sufficiently large values, \ie, of the order of $O(1)$.

Rene Vidal, Yi Ma, Shankar Sastry

This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high- dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as K-subspaces and Expectation Maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.