  Intelligent agents can cope with sensory-rich environments by learning
task-agnostic state abstractions. In this paper, we propose an algorithm to
approximate causal states, which are the coarsest partition of the joint
history of actions and observations in partially-observable Markov decision
processes (POMDP). Our method learns approximate causal state representations
from RNNs trained to predict subsequent observations given the history. We
demonstrate that these learned state representations are useful for learning
policies efficiently in reinforcement learning problems with rich observation
spaces. We connect causal states with causal feature sets from the causal
inference literature, and also provide theoretical guarantees on the optimality
of the continuous version of this causal state representation under Lipschitz
assumptions by proving equivalence to bisimulation, a relation between
behaviorally equivalent systems. This allows for lower bounds on the optimal
value function of the learned representation, which is tight given certain
assumptions. Finally, we empirically evaluate causal state representations
using multiple partially observable tasks and compare with prior methods.
