arXiv subjects

Lasse Peters

Publications and source records attributed to Lasse Peters.

At least 19 recordsLinked to original sources

arXiv2026

Coordinated Diffusion: Generating Multi-Agent Behavior Without Multi-Agent Demonstrations

Imitation learning powered by generative models has proven effective for modeling complex single-agent behaviors. However, teaching multi-agent systems, like multiple arms or vehicles, to coordinate through imitation learning is hindered by a fundamental data bottleneck: as the joint state-action space grows exponentially with the number of agents, collecting a sufficient amount of coordinated multi-agent demonstrations becomes extremely costly. In this work, we ask: how can we leverage single-agent demonstration data to learn multi-agent policies? We present Coordinated Diffusion (CoDi), a framework that couples independently trained single-agent diffusion policies through a user-defined multi-agent cost function, without requiring any coordinated demonstrations. We derive a new diffusion-based sampling scheme wherein the diffusion score function decomposes into independent, single-agent pre-trained base policies plus a cost-driven guidance term that coordinates these base policies into cohesive multi-agent behavior. We show that this guidance term can be estimated in a gradient-free manner, making CoDi applicable to black-box, non-differentiable cost functions without additional training. Theoretically and empirically, we analyze the conditions under which this composition can faithfully approximate a target multi-agent behavior. We find a complementary role for demonstration data versus the cost function: single-agent demonstrations must cover the support of the desired multi-agent behavior, while the cost function must promote desired behavior from this product of single-agent policies. Our results in simulation and hardware experiments of a two-arm manipulation task show that CoDi discovers robust coordinated behavior from single-agent data, is more data-efficient than multi-agent baselines, and highlights the importance of joint guidance, base policy support, and cost design.

cs.RO↗

arXiv2026

Controllability in preference-conditioned multi-objective reinforcement learning

Multi-objective reinforcement learning (MORL) allows a user to express preference over outcomes in terms of the relative importance of the objectives, but standard metrics cannot capture whether changes in preference reliably change the agent's behavior in the intended way, a property termed controllability. As a result, preference-conditioned agents can score well on standard MORL metrics while being insensitive to the preference input. If the ability to control agents cannot be reliably assessed, the symbolic interface that MORL provides between user intent and agent behavior is broken. Mainstream MORL metrics alone fail to measure the controllability of preference-conditioned agents, motivating a complementary metric specifically designed to that end. We hope the results spur discussion in the community on existing evaluation protocols to consolidate advances in preference adaptation in MORL to larger and more complex problems.

cs.LG↗

arXiv2026

Homotopy-Guided Potential Games for Congestion-Aware Navigation

We address the multi-agent motion planning problem where interactions, collisions, and congestion co-exist. Conventional game-theoretic planners capture interactions among agents but often converge to conservative, congested equilibria. Homotopy planners, on the other hand, can explore topologically distinct paths, but lack mechanisms to account for the interdependence of agents' future actions. We propose a unified framework that leverages homotopy classes as structured strategy sets within a receding-horizon setup. At each planning stage, a deterministic homotopy planner generates topologically distinct paths for each agent, conditioned on the joint configuration. To avoid intractable growth of candidate paths, we propose a simple heuristic filtering step that selects a top-$K$ subset of the most suitable congestion-free joint strategies to ensure computational tractability. These serve as initializations for a potential game that enforces homotopy-consistent constraints and yields a generalized open-loop Nash equilibrium (OLNE), with penalties discouraging abrupt strategy shifts in a receding-horizon setting. Simulations with three agents demonstrate improved efficiency (faster completion) and enhanced safety (greater inter-agent clearance, leading to reduced congestion) compared to a local baseline and NH-ORCA that do not reason about homotopies. Hardware trials with two robots and one human demonstrate robustness to irrational behaviors, where our method adapts by switching to alternative feasible equilibria while the baseline game fails.

eess.SY↗

arXiv2026

Breaking Exponential Complexity in Games of Ordered Preference: A Tractable Reformulation

Games of ordered preference (GOOPs) model multi-player equilibrium problems in which each player maintains a distinct hierarchy of strictly prioritized objectives. Existing approaches solve GOOPs by deriving and enforcing the necessary optimality conditions that characterize lexicographically constrained Nash equilibria through a single-level reformulation. However, the number of primal and dual variables in the resulting KKT system grows exponentially with the number of preference levels, leading to severe scalability challenges. We derive a compact reformulation of these necessary conditions that preserves the essential primal stationarity structure across hierarchy levels, yielding a "reduced" KKT system whose size grows polynomially with both the number of players and the number of preference levels. The reduced system constitutes a relaxation of the complete KKT system, yet it remains a valid necessary condition for local GOOP equilibria. For GOOPs with quadratic objectives and linear constraints, we prove that the primal solution sets of the reduced and complete KKT systems coincide. More generally, for GOOPs with arbitrary (but smooth) nonlinear objectives and constraints, the reduced KKT conditions recover all local GOOP equilibria but may admit spurious non-equilibrium solutions. We introduce a second-order sufficient condition to certify when a candidate point corresponds to a local GOOP equilibrium. We also develop a primal-dual interior-point method for computing a local GOOP equilibrium with local quadratic convergence. The resulting framework enables scalable and efficient computation of GOOP equilibria beyond the tractable range of existing exponentially complex formulations.

cs.GT↗

arXiv2026

Strategizing at Speed: A Learned Model Predictive Game for Multi-Agent Drone Racing

Autonomous drone racing pushes the boundaries of high-speed motion planning and multi-agent strategic decision-making. Success in this domain requires drones not only to navigate at their limits but also to anticipate and counteract competitors' actions. In this paper, we study a fundamental question that arises in this domain: how deeply should an agent strategize before taking an action? To this end, we compare two planning paradigms: the Model Predictive Game (MPG), which finds interaction-aware strategies at the expense of longer computation times, and contouring Model Predictive Control (MPC), which computes strategies rapidly but does not reason about interactions. We perform extensive experiments to study this trade-off, revealing that MPG outperforms MPC at moderate velocities but loses its advantage at higher speeds due to latency. To address this shortcoming, we propose a Learned Model Predictive Game (LMPG) approach that amortizes model predictive gameplay to reduce latency. In both simulation and hardware experiments, we benchmark our approach against MPG and MPC in head-to-head races, finding that LMPG outperforms both baselines.

cs.RO↗

arXiv2026

Bayesian Inverse Games with High-Dimensional Multi-Modal Observations

Many multi-agent interaction scenarios can be naturally modeled as noncooperative games, where each agent's decisions depend on others' future actions. However, deploying game-theoretic planners for autonomous decision-making requires a specification of all agents' objectives. To circumvent this practical difficulty, recent work develops maximum likelihood techniques for solving inverse games that can identify unknown agent objectives from interaction data. Unfortunately, these methods only infer point estimates and do not quantify estimator uncertainty; correspondingly, downstream planning decisions can overconfidently commit to unsafe actions. We present an approximate Bayesian inference approach for solving the inverse game problem, which can incorporate observation data from multiple modalities and be used to generate samples from the Bayesian posterior over the hidden agent objectives given limited sensor observations in real time. Concretely, the proposed Bayesian inverse game framework trains a structured variational autoencoder with an embedded differentiable Nash game solver on interaction datasets and does not require labels of agents' true objectives. Extensive experiments show that our framework successfully learns prior and posterior distributions, improves inference quality over maximum likelihood estimation-based inverse game approaches, and enables safer downstream decision-making without sacrificing efficiency. When trajectory information is uninformative or unavailable, multimodal inference further reduces uncertainty by exploiting additional observation modalities.

cs.LG↗

arXiv2025

Approximate solutions to games of ordered preference

Autonomous vehicles must balance ranked objectives, such as minimizing travel time, ensuring safety, and coordinating with traffic. Games of ordered preference effectively model these interactions but become computationally intractable as the time horizon, number of players, or number of preference levels increase. While receding horizon frameworks mitigate long-horizon intractability by solving sequential shorter games, often warm-started, they do not resolve the complexity growth inherent in existing methods for solving games of ordered preference. This paper introduces a solution strategy that avoids excessive complexity growth by approximating solutions using lexicographic iterated best response (IBR) in receding horizon, termed "lexicographic IBR over time." Lexicographic IBR over time uses past information to accelerate convergence. We demonstrate through simulated traffic scenarios that lexicographic IBR over time efficiently computes approximate-optimal solutions for receding horizon games of ordered preference, converging towards generalized Nash equilibria.

eess.SY↗

arXiv2025

Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis

Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions that prevent future failures. While in theory, HJ reachability can synthesize safe controllers for nonlinear systems and nonconvex constraints, in practice, it has been limited to hand-engineered collision-avoidance constraints modeled via low-dimensional state-space representations and first-principles dynamics. In this work, our goal is to generalize safe robot controllers to prevent failures that are hard--if not impossible--to write down by hand, but can be intuitively identified from high-dimensional observations: for example, spilling the contents of a bag. We propose Latent Safety Filters, a latent-space generalization of HJ reachability that tractably operates directly on raw observation data (e.g., RGB images) to automatically compute safety-preserving actions without explicit recovery demonstrations by performing safety analysis in the latent embedding space of a generative world model. Our method leverages diverse robot observation-action data of varying quality (including successes, random exploration, and unsafe demonstrations) to learn a world model. Constraint specification is then transformed into a classification problem in the latent space of the learned world model. In simulation and hardware experiments, we compute an approximation of Latent Safety Filters to safeguard arbitrary policies (from imitation- learned policies to direct teleoperation) from complex safety hazards, like preventing a Franka Research 3 manipulator from spilling the contents of a bag or toppling cluttered objects.

cs.RO↗

arXiv2024

You Can't Always Get What You Want: Games of Ordered Preference

We study noncooperative games, in which each player's objective is composed of a sequence of ordered- and potentially conflicting-preferences. Problems of this type naturally model a wide variety of scenarios: for example, drivers at a busy intersection must balance the desire to make forward progress with the risk of collision. Mathematically, these problems possess a nested structure, and to behave properly players must prioritize their most important preference, and only consider less important preferences to the extent that they do not compromise performance on more important ones. We consider multi-agent, noncooperative variants of these problems, and seek generalized Nash equilibria in which each player's decision reflects both its hierarchy of preferences and other players' actions. We make two key contributions. First, we develop a recursive approach for deriving the first-order optimality conditions of each player's nested problem. Second, we propose a sequence of increasingly tight relaxations, each of which can be transcribed as a mixed complementarity problem and solved via existing methods. Experimental results demonstrate that our approach reliably converges to equilibrium solutions that strictly reflect players' individual ordered preferences.

cs.GT↗

arXiv2024

Updating Robot Safety Representations Online from Natural Language Feedback

Robots must operate safely when deployed in novel and human-centered environments, like homes. Current safe control approaches typically assume that the safety constraints are known a priori, and thus, the robot can pre-compute a corresponding safety controller. While this may make sense for some safety constraints (e.g., avoiding collision with walls by analyzing a floor plan), other constraints are more complex (e.g., spills), inherently personal, context-dependent, and can only be identified at deployment time when the robot is interacting in a specific environment and with a specific person (e.g., fragile objects, expensive rugs). Here, language provides a flexible mechanism to communicate these evolving safety constraints to the robot. In this work, we use vision language models (VLMs) to interpret language feedback and the robot's image observations to continuously update the robot's representation of safety constraints. With these inferred constraints, we update a Hamilton-Jacobi reachability safety controller online via efficient warm-starting techniques. Through simulation and hardware experiments, we demonstrate the robot's ability to infer and respect language-based safety constraints with the proposed approach.

cs.RO↗

arXiv2024

Auto-Encoding Bayesian Inverse Games

When multiple agents interact in a common environment, each agent's actions impact others' future decisions, and noncooperative dynamic games naturally capture this coupling. In interactive motion planning, however, agents typically do not have access to a complete model of the game, e.g., due to unknown objectives of other players. Therefore, we consider the inverse game problem, in which some properties of the game are unknown a priori and must be inferred from observations. Existing maximum likelihood estimation (MLE) approaches to solve inverse games provide only point estimates of unknown parameters without quantifying uncertainty, and perform poorly when many parameter values explain the observed behavior. To address these limitations, we take a Bayesian perspective and construct posterior distributions of game parameters. To render inference tractable, we employ a variational autoencoder (VAE) with an embedded differentiable game solver. This structured VAE can be trained from an unlabeled dataset of observed interactions, naturally handles continuous, multi-modal distributions, and supports efficient sampling from the inferred posteriors without computing game solutions at runtime. Extensive evaluations in simulated driving scenarios demonstrate that the proposed approach successfully learns the prior and posterior game parameter distributions, provides more accurate objective estimates than MLE baselines, and facilitates safer and more efficient game-theoretic motion planning.

cs.RO↗

arXiv2023

Contingency Games for Multi-Agent Interaction

Contingency planning, wherein an agent generates a set of possible plans conditioned on the outcome of an uncertain event, is an increasingly popular way for robots to act under uncertainty. In this work we take a game-theoretic perspective on contingency planning, tailored to multi-agent scenarios in which a robot's actions impact the decisions of other agents and vice versa. The resulting contingency game allows the robot to efficiently interact with other agents by generating strategic motion plans conditioned on multiple possible intents for other actors in the scene. Contingency games are parameterized via a scalar variable which represents a future time when intent uncertainty will be resolved. By estimating this parameter online, we construct a game-theoretic motion planner that adapts to changing beliefs while anticipating future certainty. We show that existing variants of game-theoretic planning under uncertainty are readily obtained as special cases of contingency games. Through a series of simulated autonomous driving scenarios, we demonstrate that contingency games close the gap between certainty-equivalent games that commit to a single hypothesis and non-contingent multi-hypothesis games that do not account for future uncertainty reduction.

cs.RO↗

arXiv2023

Scenario-Game ADMM: A Parallelized Scenario-Based Solver for Stochastic Noncooperative Games

Decision-making in multi-player games can be extremely challenging, particularly under uncertainty. In this work, we propose a new sample-based approximation to a class of stochastic, general-sum, pure Nash games, where each player has an expected-value objective and a set of chance constraints. This new approximation scheme inherits the accuracy of objective approximation from the established sample average approximation (SAA) method and enjoys a feasibility guarantee derived from the scenario optimization literature. We characterize the sample complexity of this new game-theoretic approximation scheme, and observe that high accuracy usually requires a large number of samples, which results in a large number of sampled constraints. To accommodate this, we decompose the approximated game into a set of smaller games with few constraints for each sampled scenario, and propose a decentralized, consensus-based ADMM algorithm to efficiently compute a generalized Nash equilibrium (GNE) of the approximated game. We prove the convergence of our algorithm to a GNE and empirically demonstrate superior performance relative to a recent baseline algorithm based on ADMM and interior point method.

eess.SY↗

arXiv2023

Online and Offline Learning of Player Objectives from Partial Observations in Dynamic Games

Robots deployed to the real world must be able to interact with other agents in their environment. Dynamic game theory provides a powerful mathematical framework for modeling scenarios in which agents have individual objectives and interactions evolve over time. However, a key limitation of such techniques is that they require a-priori knowledge of all players' objectives. In this work, we address this issue by proposing a novel method for learning players' objectives in continuous dynamic games from noise-corrupted, partial state observations. Our approach learns objectives by coupling the estimation of unknown cost parameters of each player with inference of unobserved states and inputs through Nash equilibrium constraints. By coupling past state estimates with future state predictions, our approach is amenable to simultaneous online learning and prediction in receding horizon fashion. We demonstrate our method in several simulated traffic scenarios in which we recover players' preferences for, e.g., desired travel speed and collision-avoidance behavior. Results show that our method reliably estimates game-theoretic models from noise-corrupted data that closely matches ground-truth objectives, consistently outperforming state-of-the-art approaches.

cs.RO↗

arXiv2023

Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories

In multi-agent dynamic games, the Nash equilibrium state trajectory of each agent is determined by its cost function and the information pattern of the game. However, the cost and trajectory of each agent may be unavailable to the other agents. Prior work on using partial observations to infer the costs in dynamic games assumes an open-loop information pattern. In this work, we demonstrate that the feedback Nash equilibrium concept is more expressive and encodes more complex behavior. It is desirable to develop specific tools for inferring players' objectives in feedback games. Therefore, we consider the dynamic game cost inference problem under the feedback information pattern, using only partial state observations and incomplete trajectory data. To this end, we first propose an inverse feedback game loss function, whose minimizer yields a feedback Nash equilibrium state trajectory closest to the observation data. We characterize the landscape and differentiability of the loss function. Given the difficulty of obtaining the exact gradient, our main contribution is an efficient gradient approximator, which enables a novel inverse feedback game solver that minimizes the loss using first-order optimization. In thorough empirical evaluations, we demonstrate that our algorithm converges reliably and has better robustness and generalization performance than the open-loop baseline method when the observation data reflects a group of players acting in a feedback Nash game.

cs.MA↗

arXiv2022

Learning to Play Trajectory Games Against Opponents with Unknown Objectives

Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in such interactive settings. However, tractable algorithms for such problems usually rely on a strong assumption, namely that the objectives of all players in the scene are known. To make such tools applicable for ego-centric planning with only local information, we propose an adaptive model-predictive game solver, which jointly infers other players' objectives online and computes a corresponding generalized Nash equilibrium (GNE) strategy. The adaptivity of our approach is enabled by a differentiable trajectory game solver whose gradient signal is used for maximum likelihood estimation (MLE) of opponents' objectives. This differentiability of our pipeline facilitates direct integration with other differentiable elements, such as neural networks (NNs). Furthermore, in contrast to existing solvers for cost inference in games, our method handles not only partial state observations but also general inequality constraints. In two simulated traffic scenarios, we find superior performance of our approach over both existing game-theoretic methods and non-game-theoretic model-predictive control (MPC) approaches. We also demonstrate our approach's real-time planning capabilities and robustness in two hardware experiments.

cs.RO↗

arXiv2022

Learning Mixed Strategies in Trajectory Games

In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior. Trajectory games capture these complex effects by design. In competitive settings, this makes them a more faithful interaction model than traditional "predict then plan" approaches. However, current game-theoretic planning methods have important limitations. In this work, we propose two main contributions. First, we introduce an offline training phase which reduces the online computational burden of solving trajectory games. Second, we formulate a lifted game which allows players to optimize multiple candidate trajectories in unison and thereby construct more competitive "mixed" strategies. We validate our approach on a number of experiments using the pursuit-evasion game "tag."

cs.GT↗

arXiv2021

Inferring Objectives in Continuous Dynamic Games from Noise-Corrupted Partial State Observations

Robots and autonomous systems must interact with one another and their environment to provide high-quality services to their users. Dynamic game theory provides an expressive theoretical framework for modeling scenarios involving multiple agents with differing objectives interacting over time. A core challenge when formulating a dynamic game is designing objectives for each agent that capture desired behavior. In this paper, we propose a method for inferring parametric objective models of multiple agents based on observed interactions. Our inverse game solver jointly optimizes player objectives and continuous-state estimates by coupling them through Nash equilibrium constraints. Hence, our method is able to directly maximize the observation likelihood rather than other non-probabilistic surrogate criteria. Our method does not require full observations of game states or player strategies to identify player objectives. Instead, it robustly recovers this information from noisy, partial state observations. As a byproduct of estimating player objectives, our method computes a Nash equilibrium trajectory corresponding to those objectives. Thus, it is suitable for downstream trajectory forecasting tasks. We demonstrate our method in several simulated traffic scenarios. Results show that it reliably estimates player objectives from a short sequence of noise-corrupted partial state observations. Furthermore, using the estimated objectives, our method makes accurate predictions of each player's trajectory.

cs.RO↗