  We consider offline reinforcement learning (RL) with heterogeneous agents
under severe data scarcity, i.e., we only observe a single historical
trajectory for every agent under an unknown, potentially sub-optimal policy. We
find that the performance of state-of-the-art offline and model-based RL
methods degrade significantly given such limited data availability, even for
commonly perceived "solved" benchmark settings such as "MountainCar" and
"CartPole". To address this challenge, we propose PerSim, a model-based offline
RL approach which first learns a personalized simulator for each agent by
collectively using the historical trajectories across all agents, prior to
learning a policy. We do so by positing that the transition dynamics across
agents can be represented as a latent function of latent factors associated
with agents, states, and actions; subsequently, we theoretically establish that
this function is well-approximated by a "low-rank" decomposition of separable
agent, state, and action latent functions. This representation suggests a
simple, regularized neural network architecture to effectively learn the
transition dynamics per agent, even with scarce, offline data. We perform
extensive experiments across several benchmark environments and RL methods. The
consistent improvement of our approach, measured in terms of both state
dynamics prediction and eventual reward, confirms the efficacy of our framework
in leveraging limited historical data to simultaneously learn personalized
policies across agents.
