arXiv subjects

Lasse Peters

Publications and source records attributed to Lasse Peters.

24 records · Page 2Linked to original sources

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 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↗

arXiv2020

Inference-Based Strategy Alignment for General-Sum Differential Games

In many settings where multiple agents interact, the optimal choices for each agent depend heavily on the choices of the others. These coupled interactions are well-described by a general-sum differential game, in which players have differing objectives, the state evolves in continuous time, and optimal play may be characterized by one of many equilibrium concepts, e.g., a Nash equilibrium. Often, problems admit multiple equilibria. From the perspective of a single agent in such a game, this multiplicity of solutions can introduce uncertainty about how other agents will behave. This paper proposes a general framework for resolving ambiguity between equilibria by reasoning about the equilibrium other agents are aiming for. We demonstrate this framework in simulations of a multi-player human-robot navigation problem that yields two main conclusions: First, by inferring which equilibrium humans are operating at, the robot is able to predict trajectories more accurately, and second, by discovering and aligning itself to this equilibrium the robot is able to reduce the cost for all players.

cs.RO↗

arXiv2020

iLQGames.jl: Rapidly Designing and Solving Differential Games in Julia

In many problems that involve multiple decision making agents, optimal choices for each agent depend on the choices of others. Differential game theory provides a principled formalism for expressing these coupled interactions and recent work offers efficient approximations to solve these problems to non-cooperative equilibria. iLQGames.jl is a framework for designing and solving differential games, built around the iterative linear-quadratic method. It is written in the Julia programming language to allow flexible prototyping and integration with other research software, while leveraging the high-performance nature of the language to allow real-time execution. The open-source software package can be found at https://github.com/lassepe/iLQGames.jl.

cs.MA↗

arXiv2020

Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Games

Many problems in robotics involve multiple decision making agents. To operate efficiently in such settings, a robot must reason about the impact of its decisions on the behavior of other agents. Differential games offer an expressive theoretical framework for formulating these types of multi-agent problems. Unfortunately, most numerical solution techniques scale poorly with state dimension and are rarely used in real-time applications. For this reason, it is common to predict the future decisions of other agents and solve the resulting decoupled, i.e., single-agent, optimal control problem. This decoupling neglects the underlying interactive nature of the problem; however, efficient solution techniques do exist for broad classes of optimal control problems. We take inspiration from one such technique, the iterative linear-quadratic regulator (ILQR), which solves repeated approximations with linear dynamics and quadratic costs. Similarly, our proposed algorithm solves repeated linear-quadratic games. We experimentally benchmark our algorithm in several examples with a variety of initial conditions and show that the resulting strategies exhibit complex interactive behavior. Our results indicate that our algorithm converges reliably and runs in real-time. In a three-player, 14-state simulated intersection problem, our algorithm initially converges in < 0.25s. Receding horizon invocations converge in < 50 ms in a hardware collision-avoidance test.

eess.SY↗