Xinjie Liu

Xinjie Liu, Lasse Peters, Javier Alonso-Mora et al.

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.

Xinjie Liu, Cyrus Neary, Kushagra Gupta et al.

Many reinforcement learning (RL) algorithms are impractical for deployment in operational systems or for training with computationally expensive high-fidelity simulations, as they require large amounts of data. Meanwhile, low-fidelity simulators -- such as reduced-order models, heuristic rewards, or generative world models -- can cheaply provide useful data for RL training, even if they are too coarse for zero-shot transfer. We propose multi-fidelity policy gradients (MFPGs), an RL framework that mixes a small amount of data from the target environment with a control variate formed from a large volume of low-fidelity simulation data to construct an unbiased, variance-reduced estimator for on-policy policy gradients. We instantiate the framework with a multi-fidelity variant of the classical REINFORCE algorithm. We show that under standard assumptions, the MFPG estimator guarantees asymptotic convergence of REINFORCE to locally optimal policies in the target environment, and achieves faster finite-sample convergence rates compared to training with high-fidelity data alone. Empirically, we evaluate the MFPG algorithm across a suite of simulated robotics benchmark tasks with limited high-fidelity data but abundant off-dynamics, low-fidelity data. With mild-moderate dynamics gaps, MFPG reliably improves the median performance over a high-fidelity-only baseline, matching the performance of leading multi-fidelity baselines despite its simplicity and minimal tuning overhead. Under large dynamics gaps, MFPG demonstrates the strongest robustness among the evaluated multi-fidelity approaches. An additional experiment shows that MFPG can remain effective even under low-fidelity reward misspecification. Thus, MFPG not only offers a novel paradigm for efficient sim-to-real transfer but also provides a principled approach to managing the trade-off between policy performance and data collection costs.