Two stochastic dynamic programming problems by model-free actor-critic recurrent-network learning in non-Markovian settings

We describe two stochastic non-Markovian dynamic programming (DP) problems, showing how the posed problems can be attacked by using actor-critic reinforcement learning with recurrent neural networks (RNN). We assume that the current state of a dynamical system is "completely observable", but that the rules, unknown to our decision-making agent, for the current reward and state transition depend not only on current state and action, but on possibly the "entire history" of past states and actions. This should not be confused with problems of "partially observable Markov decision processes (POMDPs)", where the current state is only deduced from either partial (observable) state alone or error-corrupted observations. Our actor-critic RNN agent is capable of finding an optimal policy, while learning neither transitional probabilities, associated rewards, nor by how much the current state space must be augmented so that the Markov property holds. The RNN\´s recurrent connections or context units function as an "implicit" history memory (or internal state) to develop "sensitivity" to non-Markovian dependencies, rendering the process Markovian implicitly and automatically in a "totally model-free" fashion. In particular, using two small-scale longest-path problems in a stochastic non-Markovian setting, we discuss model-free learning features in comparison with the model-based approach by the classical DP algorithm.