Learning Reward Machines from Non-Markov Reward Functions to Represent Complex Reward Dynamics

Core Concepts

This paper proposes a framework for mapping non-Markov reward functions into equivalent Markov representations by learning a specialized reward automaton called a Reward Machine (RM). The approach learns RMs without requiring access to a set of high-level propositional symbols, instead inferring hidden triggers directly from data.

Abstract

The paper addresses the challenge of reinforcement learning (RL) algorithms that assume a Markov reward function, when in complex environments the reward function may not be Markov. To address this, the authors propose a framework for mapping non-Markov reward functions into equivalent Markov representations by learning a specialized reward automaton called a Reward Machine (RM).
Key highlights:

RMs are more expressive than Deterministic Finite-State Automata (DFAs) as they can represent complex reward behavior in a single automaton, rather than requiring multiple DFAs.
The authors do not require access to a set of high-level propositional symbols and a labeling function, which is a limitation of prior work. Instead, they infer hidden triggers directly from data that encode the non-Markov reward dynamics.
The mapping process is formulated as an Integer Linear Programming (ILP) problem, which allows for powerful off-the-shelf discrete optimization solvers.
The authors prove that the Abstract Reward Markov Decision Process (ARMDP), which is the cross-product of the RM and the observed state space, is a suitable representation for maximizing reward expectations under non-Markov rewards.
Experiments on the Officeworld and Breakfastworld domains demonstrate the effectiveness of the approach, particularly in learning RMs with interdependent reward signals.

Stats

The paper does not provide any specific numerical data or metrics to support the key claims. The results are presented qualitatively through figures and descriptions of the learning performance and properties of the learned representations.

Quotes

"RMs are particularly appealing as they offer succinct encoding of non-Markov reward behavior and task decomposition."
"By learning RMs we can model reward dependencies in a single automata by representing patterns in H = (S × A × R)∗."
"Importantly, we show how by leveraging H = (S × A × R)∗ we can expedite learning in these cases."

Key Insights Distilled From

Detecting Hidden Triggers: Mapping Non-Markov Reward Functions to Markov

by Gregory Hyde... at arxiv.org 05-01-2024

https://arxiv.org/pdf/2401.11325.pdf

Deeper Inquiries

How could the proposed approach be extended to handle continuous state and action spaces, beyond the discrete domains considered in this work

To extend the proposed approach to handle continuous state and action spaces, we can leverage techniques from deep learning, specifically Recurrent Neural Networks (RNNs) or Long Short-Term Memory (LSTM) networks. By incorporating RNNs or LSTMs, we can capture the sequential nature of the data and handle continuous variables effectively. These neural network architectures can learn representations of the state and action spaces in a continuous manner, allowing for more complex and continuous state-action mappings.
Additionally, we can use techniques like autoencoders or variational autoencoders to learn a compressed representation of the continuous state and action spaces. By encoding the continuous variables into a lower-dimensional latent space, we can reduce the complexity of the problem while retaining important information for decision-making.
Furthermore, incorporating techniques from imitation learning or inverse reinforcement learning can help in learning the underlying structure of the continuous state and action spaces from expert demonstrations or behavioral data. By leveraging these approaches, we can enhance the interpretability and generalizability of the learned reward functions in continuous domains.

What are the potential limitations or drawbacks of the ARMDP representation, and how might they be addressed in future research

One potential limitation of the ARMDP representation is the scalability and computational complexity when dealing with large state and action spaces. As the size of the state and action spaces increases, the number of possible transitions and reward dependencies grows exponentially, leading to challenges in solving the ILP efficiently.
To address this limitation, future research could focus on developing more efficient optimization algorithms tailored for large-scale ARMDP problems. Techniques like parallel computing, distributed optimization, or approximation methods could be explored to handle the computational demands of scaling up the ARMDP representation.
Another drawback could be the interpretability of the learned RMs in complex environments. As the number of hidden triggers and reward dependencies increases, understanding the underlying logic of the automaton may become challenging. Future research could investigate visualization techniques or explainable AI methods to enhance the interpretability of the learned RMs.

Could the insights from learning RMs provide useful guidance for designing more interpretable reward functions in reinforcement learning, beyond just representing non-Markov dynamics

The insights from learning Reward Machines (RMs) can indeed provide valuable guidance for designing more interpretable reward functions in reinforcement learning beyond just representing non-Markov dynamics. By leveraging the structured and symbolic nature of RMs, researchers can design reward functions that capture complex dependencies and patterns in the environment.
One way to utilize these insights is to incorporate domain knowledge and expert input when designing reward functions. By encoding domain-specific rules and constraints into the RM structure, we can create reward functions that align with the desired behavior and objectives in a more interpretable manner.
Additionally, the concept of hidden triggers and reward dependencies in RMs can inspire the development of modular and decomposable reward functions. By breaking down the reward function into smaller components that interact based on specific triggers, we can create more transparent and understandable reward structures.
Furthermore, the interpretability of RMs can guide the design of reward shaping techniques that provide meaningful feedback to the learning agent. By shaping the reward signal based on the learned dependencies and triggers, we can steer the agent towards desired behaviors while maintaining transparency and interpretability in the learning process.