We propose an approach to simulating trajectories of multiple interacting agents (road users) based on transformers and probabilistic graphical models (PGMs), and apply it to the Waymo SimAgents challenge. The transformer baseline is based on the MTR model, which predicts multiple future trajectories conditioned on the past trajectories and static road layout features. We then improve upon these generated trajectories using a PGM, which contains factors which encode prior knowledge, such as a preference for smooth trajectories, and avoidance of collisions with static obstacles and other moving agents. We perform (approximate) MAP inference in this PGM using the Gauss-Newton method. Finally we sample $K=32$ trajectories for each of the $N \sim 100$ agents for the next $T=8 \Delta$ time steps, where $\Delta=10$ is the sampling rate per second. Following the Model Predictive Control (MPC) paradigm, we only return the first element of our forecasted trajectories at each step, and then we replan, so that the simulation can constantly adapt to its changing environment. We therefore call our approach "Model Predictive Simulation" or MPS. We show that MPS improves upon the MTR baseline, especially in safety critical metrics such as collision rate. Furthermore, our approach is compatible with any underlying forecasting model, and does not require extra training, so we believe it is a valuable contribution to the community.

We consider the problem of recovering a latent graph where the observations at each node are \emph{aliased}, and transitions are stochastic. Observations are gathered by an agent traversing the graph. Aliasing means that multiple nodes emit the same observation, so the agent can not know in which node it is located. The agent needs to uncover the hidden topology as accurately as possible and in as few steps as possible. This is equivalent to efficient recovery of the transition probabilities of a partially observable Markov decision process (POMDP) in which the observation probabilities are known. An algorithm for efficiently exploring (and ultimately recovering) the latent graph is provided. Our approach is exponentially faster than naive exploration in a variety of challenging topologies with aliased observations while remaining competitive with existing baselines in the unaliased regime.