Abstract Tabular reinforcement learning methods cannot operate directly on continuous state spaces. One solution to this problem is to partition the state space. A good partitioning enables generalization during learning and more efficient exploitation of prior experiences. Consequently, the learning process becomes faster and produces more reliable policies. However, partitioning introduces approximation, which is particularly harmful in the presence of nonlinear relations between state components. An ideal partition should be as coarse as possible, while capturing the key structure of the state space for the given problem. This work extracts partitions from the environment dynamics by symbolic execution. We show that symbolic partitioning improves state space coverage with respect to environmental behavior and allows reinforcement learning to perform better for sparse rewards. We evaluate symbolic state space partitioning with respect to precision, scalability, learning agent performance and state space coverage for the learned policies.

The development process for reinforcement learning applications is still exploratory rather than systematic. This exploratory nature reduces reuse of specifications between applications and increases the chances of introducing programming errors. This paper takes a step towards systematizing the development of reinforcement learning applications. We introduce a formal specification of reinforcement learning problems and algorithms, with a particular focus on temporal difference methods and their definitions in backup diagrams. We further develop a test harness for a large class of reinforcement learning applications based on temporal difference learning, including SARSA and Q-learning. The entire development is rooted in functional programming methods; starting with pure specifications and denotational semantics, ending with property-based testing and using compositional interpreters for a domain-specific term language as a test oracle for concrete implementations. We demonstrate the usefulness of this testing method on a number of examples, and evaluate with mutation testing. We show that our test suite is effective in killing mutants (90% mutants killed for 75% of subject agents). More importantly, almost half of all mutants are killed by generic write-once-use-everywhere tests that apply to any reinforcement learning problem modeled using our library, without any additional effort from the programmer.