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While robust optimal control theory provides a rigorous framework to compute robot control policies that are provably safe, it struggles to scale to high-dimensional problems, leading to increased use of deep learning for tractable synthesis of robot safety. Unfortunately, existing neural safety synthesis methods often lack convergence guarantees and solution interpretability. In this paper, we present Minimax Actors Guided by Implicit Critic Stackelberg (MAGICS), a novel adversarial reinforcement learning (RL) algorithm that guarantees local convergence to a minimax equilibrium solution. We then build on this approach to provide local convergence guarantees for a general deep RL-based robot safety synthesis algorithm. Through both simulation studies on OpenAI Gym environments and hardware experiments with a 36-dimensional quadruped robot, we show that MAGICS can yield robust control policies outperforming the state-of-the-art neural safety synthesis methods., Comment: Algorithmic Foundations of Robotics (WAFR) XVI

Non-cooperative interactions commonly occur in multi-agent scenarios such as car racing, where an ego vehicle can choose to overtake the rival, or stay behind it until a safe overtaking "corridor" opens. While an expert human can do well at making such time-sensitive decisions, the development of safe and efficient game-theoretic trajectory planners capable of rapidly reasoning discrete options is yet to be fully addressed. The recently developed nonlinear opinion dynamics (NOD) show promise in enabling fast opinion formation and avoiding safety-critical deadlocks. However, it remains an open challenge to determine the model parameters of NOD automatically and adaptively, accounting for the ever-changing environment of interaction. In this work, we propose for the first time a learning-based, game-theoretic approach to synthesize a Neural NOD model from expert demonstrations, given as a dataset containing (possibly incomplete) state and action trajectories of interacting agents. The learned NOD can be used by existing dynamic game solvers to plan decisively while accounting for the predicted change of other agents' intents, thus enabling situational awareness in planning. We demonstrate Neural NOD's ability to make fast and robust decisions in a simulated autonomous racing example, leading to tangible improvements in safety and overtaking performance over state-of-the-art data-driven game-theoretic planning methods.

Generating realistic and controllable agent behaviors in traffic simulation is crucial for the development of autonomous vehicles. This problem is often formulated as imitation learning (IL) from real-world driving data by either directly predicting future trajectories or inferring cost functions with inverse optimal control. In this paper, we draw a conceptual connection between IL and diffusion-based generative modeling and introduce a novel framework Versatile Behavior Diffusion (VBD) to simulate interactive scenarios with multiple traffic participants. Our model not only generates scene-consistent multi-agent interactions but also enables scenario editing through multi-step guidance and refinement. Experimental evaluations show that VBD achieves state-of-the-art performance on the Waymo Sim Agents benchmark. In addition, we illustrate the versatility of our model by adapting it to various applications. VBD is capable of producing scenarios conditioning on priors, integrating with model-based optimization, sampling multi-modal scene-consistent scenarios by fusing marginal predictions, and generating safety-critical scenarios when combined with a game-theoretic solver.

As intelligent robots like autonomous vehicles become increasingly deployed in the presence of people, the extent to which these systems should leverage model-based game-theoretic planners versus data-driven policies for safe, interaction-aware motion planning remains an open question. Existing dynamic game formulations assume all agents are task-driven and behave optimally. However, in reality, humans tend to deviate from the decisions prescribed by these models, and their behavior is better approximated under a noisy-rational paradigm. In this work, we investigate a principled methodology to blend a data-driven reference policy with an optimization-based game-theoretic policy. We formulate KLGame, an algorithm for solving non-cooperative dynamic game with Kullback-Leibler (KL) regularization with respect to a general, stochastic, and possibly multi-modal reference policy. Our method incorporates, for each decision maker, a tunable parameter that permits modulation between task-driven and data-driven behaviors. We propose an efficient algorithm for computing multi-modal approximate feedback Nash equilibrium strategies of KLGame in real time. Through a series of simulated and real-world autonomous driving scenarios, we demonstrate that KLGame policies can more effectively incorporate guidance from the reference policy and account for noisily-rational human behaviors versus non-regularized baselines. Website with additional information, videos, and code: https://kl-games.github.io/., Comment: 20 pages, 12 figures

Large language models (LLMs) exhibit advanced reasoning skills, enabling robots to comprehend natural language instructions and strategically plan high-level actions through proper grounding. However, LLM hallucination may result in robots confidently executing plans that are misaligned with user goals or, in extreme cases, unsafe. Additionally, inherent ambiguity in natural language instructions can induce task uncertainty, particularly in situations where multiple valid options exist. To address this issue, LLMs must identify such uncertainty and proactively seek clarification. This paper explores the concept of introspective planning as a systematic method for guiding LLMs in forming uncertainty--aware plans for robotic task execution without the need for fine-tuning. We investigate uncertainty quantification in task-level robot planning and demonstrate that introspection significantly improves both success rates and safety compared to state-of-the-art LLM-based planning approaches. Furthermore, we assess the effectiveness of introspective planning in conjunction with conformal prediction, revealing that this combination yields tighter confidence bounds, thereby maintaining statistical success guarantees with fewer superfluous user clarification queries. Code is available at https://github.com/kevinliang888/IntroPlan., Comment: 27 pages, 11 figures. Code is available at https://github.com/kevinliang888/IntroPlan

We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane generator mapping the problem data and previous iterates to cutting planes. We propose a CPL implementation to generate split cuts, and by combining several CPLs, we devise a differentiable cutting-plane algorithm that exploits the repeated nature of parametric instances. In an offline phase, we train our algorithm by updating the internal parameters controlling the CPLs, thus altering cut generation. Once trained, our algorithm computes, with predictable execution times and a fixed number of cuts, solutions with low integrality gaps. Preliminary computational tests show that our algorithm generalizes on unseen instances and captures underlying parametric structures., Comment: Fixed missing acronyms due to glossary package. This version is analogous to the previous one, up to acronyms fixes

Recent years have seen significant progress in the realm of robot autonomy, accompanied by the expanding reach of robotic technologies. However, the emergence of new deployment domains brings unprecedented challenges in ensuring safe operation of these systems, which remains as crucial as ever. While traditional model-based safe control methods struggle with generalizability and scalability, emerging data-driven approaches tend to lack well-understood guarantees, which can result in unpredictable catastrophic failures. Successful deployment of the next generation of autonomous robots will require integrating the strengths of both paradigms. This article provides a review of safety filter approaches, highlighting important connections between existing techniques and proposing a unified technical framework to understand, compare, and combine them. The new unified view exposes a shared modular structure across a range of seemingly disparate safety filter classes and naturally suggests directions for future progress towards more scalable synthesis, robust monitoring, and efficient intervention., Comment: Accepted for publication in Annual Review of Control, Robotics, and Autonomous Systems

We present a multi-agent decision-making framework for the emergent coordination of autonomous agents whose intents are initially undecided. Dynamic non-cooperative games have been used to encode multi-agent interaction, but ambiguity arising from factors such as goal preference or the presence of multiple equilibria may lead to coordination issues, ranging from the "freezing robot" problem to unsafe behavior in safety-critical events. The recently developed nonlinear opinion dynamics (NOD) provide guarantees for breaking deadlocks. However, choosing the appropriate model parameters automatically in general multi-agent settings remains a challenge. In this paper, we first propose a novel and principled procedure for synthesizing NOD based on the value functions of dynamic games conditioned on agents' intents. In particular, we provide for the two-player two-option case precise stability conditions for equilibria of the game-induced NOD based on the mismatch between agents' opinions and their game values. We then propose an optimization-based trajectory optimization algorithm that computes agents' policies guided by the evolution of opinions. The efficacy of our method is illustrated with a simulated toll station coordination example.

We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non-cooperative potential games, i.e., the parameters of the agents' optimization problems. Our technique combines (i.) an active-set step that enforces that the agents play at a Nash equilibrium and (ii.) an implicit-differentiation step to update the estimates of the rationality parameters. We detail the convergence properties of our algorithm and perform numerical experiments on Cournot and congestion games, showing that our algorithm effectively finds high-quality solutions (in terms of out-of-sample loss) and scales to large datasets.

The deployment of robots in uncontrolled environments requires them to operate robustly under previously unseen scenarios, like irregular terrain and wind conditions. Unfortunately, while rigorous safety frameworks from robust optimal control theory scale poorly to high-dimensional nonlinear dynamics, control policies computed by more tractable "deep" methods lack guarantees and tend to exhibit little robustness to uncertain operating conditions. This work introduces a novel approach enabling scalable synthesis of robust safety-preserving controllers for robotic systems with general nonlinear dynamics subject to bounded modeling error by combining game-theoretic safety analysis with adversarial reinforcement learning in simulation. Following a soft actor-critic scheme, a safety-seeking fallback policy is co-trained with an adversarial "disturbance" agent that aims to invoke the worst-case realization of model error and training-to-deployment discrepancy allowed by the designer's uncertainty. While the learned control policy does not intrinsically guarantee safety, it is used to construct a real-time safety filter (or shield) with robust safety guarantees based on forward reachability rollouts. This shield can be used in conjunction with a safety-agnostic control policy, precluding any task-driven actions that could result in loss of safety. We evaluate our learning-based safety approach in a 5D race car simulator, compare the learned safety policy to the numerically obtained optimal solution, and empirically validate the robust safety guarantee of our proposed safety shield against worst-case model discrepancy., Comment: Accepted in 5th Annual Learning for Dynamics & Control Conference (L4DC), University of Pennsylvania

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting., Comment: 27 pages, 17 figures + references and appendices, repo: https://github.com/google/BIG-bench