Source-linked AI summary
Toward Interpretable Deep Reinforcement Learning with Linear Model U-Trees
Guiliang Liu, Oliver Schulte, Wang Zhu, Qingcan Li
TL;DR
The paper addresses the difficulty of interpreting Q-function neural networks in deep reinforcement learning. It introduces Linear Model U-trees with an online learning algorithm for active play and finds that LMUT best matches the neural network on the reinforcement-learning task while supporting feature and rule analysis. The paper notes that future work should examine sampling strategies and model variants.
Problem
Q-function neural networks contain implicit knowledge that is difficult to interpret, while existing mimic-learning methods primarily address supervised learning rather than interactive DRL.
Method
The paper introduces LMUTs and a stochastic-gradient-descent online mimic-learning algorithm for approximating DRL Q functions during active interaction.
Results
LMUT achieved the best match to the neural network in reinforcement-learning task performance compared with five baselines across three environments.
Takeaways & Limitations
LMUT’s transparent tree structure supports feature-influence analysis, rule extraction, and interpretation of knowledge implicit in the neural network.
Takeaways & Limitations
Future work should explore LMUT variants, hyperparameters, and sampling strategies for active play to clarify differences between matching play performance and matching the represented function.
Abstract
from arXiv · showhide
Deep Reinforcement Learning (DRL) has achieved impressive success in many applications. A key component of many DRL models is a neural network representing a Q function, to estimate the expected cumulative reward following a state-action pair. The Q function neural network contains a lot of implicit knowledge about the RL problems, but often remains unexamined and uninterpreted. To our knowledge, this work develops the first mimic learning framework for Q functions in DRL. We introduce Linear Model U-trees (LMUTs) to approximate neural network predictions. An LMUT is learned using a novel on-line algorithm that is well-suited for an active play setting, where the mimic learner observes an ongoing interaction between the neural net and the environment. Empirical evaluation shows that an LMUT mimics a Q function substantially better than five baseline methods. The transparent tree structure of an LMUT facilitates understanding the network's learned knowledge by analyzing feature influence, extracting rules, and highlighting the super-pixels in image inputs.
1 Introduction: Mimic a Deep Reinforcement Learner
The paper extends interpretable mimic learning to deep reinforcement learning, where neural-network knowledge is difficult to explain and data arise from environment interaction rather than static datasets. It introduces LMUTs and an online learning approach for active play, then evaluates their fidelity and game-playing behavior against baselines.
- DRL policies can perform strongly while retaining implicit, difficult-to-explain knowledge in neural networks.
- Experience Training records state-action pairs and Q values during DRL training so conventional batch methods can learn a mimic model.
- Active Play generates streaming data by interacting with the environment using a mature DRL model, requiring online model updates.
- The evaluation compares LMUT with five baselines across three environments using regression fidelity and game-playing performance.
- The paper develops an interpretable mimic-learning framework for reinforcement learning and introduces LMUTs as its model-tree representation.
- The paper uses LMUT’s transparent tree structure to analyze feature influence, extract rules, and interpret learned DRL knowledge.
2 Background and Related Work
The background frames DRL as policy learning over environment interactions, with Q functions estimated by neural networks. It connects the work to soft-label mimic learning and interpretable U-tree representations for reinforcement learning.
- Reinforcement learning constructs policies that interact with environments to maximize cumulative reward, while a Q function values actions in states.
- Deep Q-Networks use neural networks to approximate Q functions and update parameters by minimizing a differentiable loss.
- Mimic learning trains an interpretable model on soft outputs produced by a complex deep neural network.
- U-trees represent observed feature-action values with a transparent tree that maps them to state or Q values.
3 Mimic Learning for Deep Reinforcement Learning
The framework offers two ways to obtain supervision for mimicking DRL Q functions: recorded training experience or active interaction with a mature model. Active Play produces labelled transitions online while balancing exploration and exploitation.
- Unlike supervised learning, DRL generates data through environment interaction rather than static input-output pairs.
- Experience Training: Experience Training records observations and actions during DRL, then obtains corresponding soft Q outputs from a mature model.
- Active Play: Active Play uses a mature DRL model to interact with the environment and generate mimic data online.
- Active Play: The active learner uses a querying function, a deep model producing Q values, and an exploration-exploitation policy based on decaying epsilon-greedy selection.
- Active Play: Each active-play step records the observation, action, reward, next observation, and mature model’s soft Q label as a transition.
- Active Play: Active Play avoids storing the full DRL training history and can reduce exposure to frequent visits to suboptimal states.
4 Learning Linear Model U-Trees
LMUTs represent Q functions with partitioned tree cells and linear models at their leaves, then learn online from interaction transitions. Training alternates data gathering, SGD weight updates, and variance-based node splitting.
- LMUT representation: Each LMUT leaf defines an input-space partition cell interpreted as a discrete state, with linear-model weights explaining predictions through feature influence.The tree can also record rewards and transition probabilities within cells to build an MDP from interaction data.
- Training procedure: Training proceeds in separate Data Gathering and Node Splitting phases.Transitions are routed to leaves, where they are collected for fitting linear models and splitting nodes.
- Node splitting: After node updating, insufficient SGD improvement triggers a candidate split, and child nodes inherit the parent weights before further updates.The algorithm evaluates distinctions and assigns the parent transition set among the resulting child nodes.
- Training procedure: For each transition, the leaf model uses state features as input and the deep model’s Q value as the supervision label.A separate LMUT is built for each action, and SGD updates each leaf’s weights using assigned transitions.
- Node splitting: The variance criterion is selected because it works well with lower time complexity than the KS test, O(n) versus O(n^2).It selects splits whose child nodes have the least Q-value variance, while efficient exploration of possible splits remains the main scalability challenge.
5 Empirical Evaluation
The evaluation compares LMUT with five baselines across three environments using regression fidelity and game-playing performance. LMUT achieves strong online performance, competitive batch-setting fidelity, and the closest game-playing performance to DQN, while some baselines face scalability or overfitting issues.
- Evaluation Setup: The study compares LMUT with CART, M5-RT, M5-MT, FIMT, and FIMT-AF across Mountain Car, Cart Pole, and Flappy Bird.Evaluation covers regression metrics and game-playing matches under experience training and active play.
- Regression Fidelity: LMUT achieves a better fit than FIMT and FIMT-AF with a much smaller model tree, especially in active play.FIMT and FIMT-AF update continuously after each datum, whereas LMUT fits minibatches at each leaf.
- Regression Fidelity: In Mountain Car and Flappy Bird, M5-RT and M5-MT perform better than LMUT, while LMUT leads in Cart Pole and remains comparably faithful.LMUT is competitive with batch methods even in the batch setting.
- Regression Fidelity: CART produces significantly more leaves without better DQN fit than M5-RT, M5-MT, or LMUT, suggesting overfitting.The comparison uses MAE, RMSE, and model-tree size as evaluation dimensions.
- Evaluation Constraints: FIMT and FIMT-AF are omitted for Flappy Bird because neither terminates on high-dimensional data; one FIMT run took 29 minutes and 10.8GB to process 10 transitions.The reported resource constraint limits online-baseline comparison in that environment.
- Learning Curves: LMUT converges quickly in Mountain Car, while its metrics fluctuate in Cart Pole and Flappy Bird before approximating the optimum within 30k transitions.Learning curves use RAE and RSE over repeated active-play experiments.
- Game-Playing Performance: Directly learned CUT converges slowly with limited performance, particularly in high-dimensional Flappy Bird.This result contrasts direct tree learning from the environment with mimic learning.
- Game-Playing Performance: LMUT achieves Game Play Performance APER closest to DQN among the mimic methods.Batch models show strong regression fidelity but can select sub-optimal actions in key scenarios; LMUT balances coverage and optimality.
6 Interpretability
LMUT makes DRL behavior interpretable through feature influence, extracted rules, and super-pixel explanations. These analyses connect tree partitions and linear models to task-relevant state and image features.
- 6.1 Feature Influence: Feature influence combines variance reduction from splits with linear-model weight importance to assess each feature's effect on Q values.Influence is aggregated across all LMUT nodes split by the feature.
- 6.1 Feature Influence: Velocity is most influential in Mountain Car, pole angle in Cart Pole, and high-influence Flappy Bird pixels cluster near the bird's likely location.Flappy Bird pixels are highlighted when influence exceeds 0.008, the mean feature influence.
- 6.2 Rule Extraction: Extracted Mountain Car rules represent partition-cell ranges and average action Q-values, explaining when momentum-building pushes should switch direction.Examples recommend right, left, then right pushes as the car progresses through distinct velocity and position states.
- 6.2 Rule Extraction: Cart Pole rules combine cart position, cart velocity, pole angle, and pole velocity to select accelerations that maintain or counter the pole's motion.The examples show right pushes for right-tilting poles and a left push when left acceleration is needed.
- 6.3 Super-pixel Explanation: For Flappy Bird, LMUT highlights influential pixels along the root-to-cell path, with the first of four images locating pipes and the bird.The remaining three images provide further information about the bird's location and velocity.
7 Conclusion
The paper presents LMUT as an interpretable mimic-learning framework for approximating DRL Q functions and analyzing their implicit knowledge. It reports the best match to the neural network among five baselines across three environments, while identifying future work on model variants and active-play sampling.
- 7 Conclusion: LMUT represents an interpretable approximation of a deep neural network's Q function and supports feature, rule, and super-pixel analysis.The framework is evaluated against five baseline methods in three reinforcement-learning environments.
- 7 Conclusion: LMUT achieved the best match to the neural network in RL-task performance among the five evaluated baseline methods.The conclusion describes this as a clear best match without reporting a numerical value here.
- 7 Conclusion: Future work includes tree pruning, broader hyper-parameter experiments, and sampling strategies for active play.Sampling strategies are intended to clarify the observed difference between matching play performance and matching the represented function.