TLDR: The paper introduces Q-PAI, a novel algorithm that applies Q-learning, a reinforcement learning technique, to passively infer Deterministic Finite Automata (DFA) from observational data. It reinterprets the Q-function as a DFA’s transition function, bridging sub-symbolic and symbolic AI. Evaluations on Tomita grammars and real-world Bluetooth Low Energy traces show Q-PAI achieves high accuracy and infers minimal DFAs, often outperforming traditional methods like RPNI and RNNs, despite lacking theoretical guarantees of convergence.
In the realm of artificial intelligence, understanding and modeling complex systems is a fundamental challenge. Many interactive systems, from software to network protocols, can be effectively represented as automata – abstract machines that define sequences of operations or states. The process of automatically constructing these automata from observations, known as automata learning or grammatical inference, is a critical area of research with wide-ranging practical applications.
Traditionally, automata inference has been dominated by symbolic AI approaches. These methods, which include active learning algorithms like Angluin’s L* and passive techniques such as RPNI, rely on explicit symbols and rules to represent knowledge. Active learning involves querying a system directly, asking if certain data sequences are accepted or if a learned automaton matches the system’s behavior. While powerful, active learning can be costly due to numerous interactions with the system and often requires unlimited access to it.
Passive learning, in contrast, is data-driven. It constructs an automaton directly from available observational data without interacting with the system. Existing passive learning methods, like constraint-solving and RPNI, are also rooted in symbolic AI. However, these methods can be computationally intensive (learning minimal automata is generally NP-complete) and may not always yield minimal or accurate results, especially with complex datasets.
A New Bridge Between AI Paradigms
This research paper, titled “Inference of Deterministic Finite Automata via Q-Learning,” explores a novel approach by leveraging sub-symbolic AI, specifically reinforcement learning, for the passive inference of Deterministic Finite Automata (DFA). Sub-symbolic AI, which includes machine learning techniques like supervised, unsupervised, and reinforcement learning, processes and learns from data using numerical methods rather than explicit symbols.
The core insight of this work is that the Q-function, a central component of Q-learning that maps state-action pairs to rewards, can be reinterpreted as the transition function of a DFA over a finite domain. This innovative perspective creates a bridge between the statistical learning capabilities of sub-symbolic methods and the formal, symbolic representations of automata.
How Q-Learning Infers Automata
The paper introduces an algorithm called Q-PAI (Q-learning-based Passive Automata Inference). In Q-PAI, the “states” for Q-learning are defined as pairs of automaton states and input letters. The “actions” that the Q-learning agent can choose are the potential successor automaton states, along with their acceptance status (final or non-final). The Q-table, which stores the utility values for these transitions, effectively learns the optimal path through the automaton.
The learning process involves an adaptive exploration strategy, where the agent dynamically adjusts its exploration probability based on the uncertainty (variance) of Q-values in a given state. This allows for more exploration in less understood areas of the state-action space. A unique aspect of Q-PAI is its double-reward structure: the Q-table is updated based on both the label of the terminal state reached and whether the constructed DFA correctly accepts the entire word. This dual feedback mechanism helps the agent learn transitions that are both locally and globally correct.
Once the Q-table is sufficiently trained, a DFA is constructed by extracting the optimal actions (transitions) and identifying final states based on the learned Q-values. The DFA is then completed with a sink state to handle undefined transitions, ensuring it is total.
Evaluation and Performance
The Q-PAI algorithm was rigorously evaluated on two types of benchmark datasets: the well-known Tomita grammars and real-world Bluetooth Low Energy (BLE) communication traces. The training sets included characteristic sets (minimal samples), AAL-generated data (simulating active learning interactions), and randomly sampled inputs.
The results demonstrate that Q-PAI effectively infers minimal DFAs with high accuracy. For most Tomita grammars, it achieved 100% accuracy, maintaining high accuracy even in more complex cases like Tomita 5 and 7. On BLE datasets, Q-learning consistently achieved over 90% accuracy, and the inferred DFAs matched the expected sizes for the devices, showcasing its robustness in modeling real-world protocols.
Compared to other approaches like Recurrent Neural Networks (RNNs) and RPNI, Q-learning often yielded more compact models than RNNs, which tend to overestimate state numbers. While RPNI is theoretically grounded, its performance was found to be highly sensitive to dataset structure and often struggled with complex or real-world inputs. Q-PAI offers a balance of interpretability, minimality, and predictive performance across both synthetic and practical domains.
Also Read:
- RLAF: Guiding Reinforcement Learning with Automaton-Based Preferences
- Integrating Causal Knowledge for Efficient Reinforcement Learning
Challenges and Future Directions
Despite its promising performance, Q-PAI faces certain challenges. The algorithm’s effectiveness is highly sensitive to the design of the reward function, requiring careful tuning. The exploration strategy can also introduce inefficiencies in large or sparse state-action spaces, potentially slowing convergence. As the size of the target DFA increases, the scalability of the Q-table could become a limiting factor due due to higher memory and computational demands. Furthermore, unlike formal algorithms such as RPNI, Q-learning lacks theoretical guarantees for convergence to the correct minimal DFA, relying instead on empirical performance.
This research marks a significant step in linking model-free reinforcement learning with formal automata representations. Future work will focus on addressing scalability, improving efficiency, and strengthening the theoretical foundations of this promising approach to automata inference. You can read the full paper here.
