Approximate information state for approximate planning and reinforcement learning in partially observed systems
This work provides a foundational framework for approximate planning and reinforcement learning in partially observed systems, which is incremental as it builds on existing information state concepts but offers tighter bounds and learnability from data.
The authors tackled the problem of planning and learning in partially observed systems by proposing a theoretical framework based on approximate information states, showing that policies computed using this framework are approximately optimal with bounded loss of optimality. They demonstrated this through multi-time scale policy gradient algorithms and numerical experiments across low, moderate, and high-dimensional environments.
We propose a theoretical framework for approximate planning and learning in partially observed systems. Our framework is based on the fundamental notion of information state. We provide two equivalent definitions of information state -- i) a function of history which is sufficient to compute the expected reward and predict its next value; ii) equivalently, a function of the history which can be recursively updated and is sufficient to compute the expected reward and predict the next observation. An information state always leads to a dynamic programming decomposition. Our key result is to show that if a function of the history (called approximate information state (AIS)) approximately satisfies the properties of the information state, then there is a corresponding approximate dynamic program. We show that the policy computed using this is approximately optimal with bounded loss of optimality. We show that several approximations in state, observation and action spaces in literature can be viewed as instances of AIS. In some of these cases, we obtain tighter bounds. A salient feature of AIS is that it can be learnt from data. We present AIS based multi-time scale policy gradient algorithms. and detailed numerical experiments with low, moderate and high dimensional environments.