Many Reinforcement Learning algorithms assume a Markov reward function to guarantee optimality. However, not all reward functions are known to be Markov. In this paper, we propose a framework for mapping non-Markov reward functions into equivalent Markov ones by learning a Reward Machine - a specialized reward automaton. Unlike the general practice of learning Reward Machines, we do not require a set of high-level propositional symbols from which to learn. Rather, we learn \emph{hidden triggers} directly from data that encode them. We demonstrate the importance of learning Reward Machines versus their Deterministic Finite-State Automata counterparts, for this task, given their ability to model reward dependencies in a single automaton. We formalize this distinction in our learning objective. Our mapping process is constructed as an Integer Linear Programming problem. We prove that our mappings provide consistent expectations for the underlying process. We empirically validate our approach by learning black-box non-Markov Reward functions in the Officeworld Domain. Additionally, we demonstrate the effectiveness of learning dependencies between rewards in a new domain, Breakfastworld.

We propose an approach to solving Markov Decision Processes with non-Markovian rewards specified in Linear Temporal Logic interpreted over finite traces (LTL-f). Our approach integrates automata representations of LTL-f formulae into compiled MDPs that can be solved by off-the-shelf MDP planners, exploiting reward shaping to help guide search. Experiments with state-of-the-art UCT-based MDP planner PROST show automata-based reward shaping to be an effective method to guide search, producing solutions of superior quality, while maintaining policy optimality guarantees.

A popular approach to solving a decision process with non-Markovian rewards (NMRDP) is to exploit a compact representation of the reward function to automatically translate the NMRDP into an equivalent Markov decision process (MDP) amenable to our favorite MDP solution method. The contribution of this paper is a representation of non-Markovian reward functions and a translation into MDP aimed at making the best possible use of state-based anytime algorithms as the solution method. By explicitly constructing and exploring only parts of the state space, these algorithms are able to trade computation time for policy quality, and have proven quite effective in dealing with large MDPs. Our representation extends future linear temporal logic (FLTL) to express rewards. Our translation has the effect of embedding model-checking in the solution method. It results in an MDP of the minimal size achievable without stepping outside the anytime framework, and consequently in better policies by the deadline.

This paper examines a number of solution methods for decision processes with non-Markovian rewards (NMRDPs). They all exploit a temporal logic specification of the reward function to automatically translate the NMRDP into an equivalent Markov decision process (MDP) amenable to well-known MDP solution methods. They differ however in the representation of the target MDP and the class of MDP solution methods to which they are suited. As a result, they adopt different temporal logics and different translations. Unfortunately, no implementation of these methods nor experimental let alone comparative results have ever been reported. This paper is the first step towards filling this gap. We describe an integrated system for solving NMRDPs which implements these methods and several variants under a common interface; we use it to compare the various approaches and identify the problem features favoring one over the other.