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.