Efficient Decision Tree Search Using a Markov Decision Process Formulation

Centrala begrepp

The core message of this article is that decision tree learning can be formulated as a Markov Decision Process (MDP) to achieve a favorable trade-off between the complexity and performance of the learned trees. By carefully controlling the action space of the MDP using a state-dependent tests generating function, the authors demonstrate that their algorithm, Dynamic Programming Decision Tree (DPDT), can find trees that are competitive with the current state-of-the-art Branch-and-Bound (BnB) solvers in terms of training accuracy, while offering a richer set of solutions along the complexity-performance Pareto front.

Sammanfattning

The article presents a novel approach to decision tree learning by formulating it as a Markov Decision Process (MDP). The key aspects are:

MDP Formulation: The authors define an MDP where the states represent subsets of the training data and the actions correspond to binary tests (splits) to be applied. The reward function encodes a trade-off between the complexity (average number of tests performed) and the training accuracy of the learned tree.

Tests Generating Function: To make the MDP tractable, the authors introduce a state-dependent tests generating function that dynamically limits the set of admissible tests at each state. They propose using the test nodes of a CART tree as the set of admissible tests, which empirically outperforms a baseline that returns the most informative splits.

Dynamic Programming Solver: The authors use dynamic programming to solve the MDP and obtain the optimal policy, which can then be converted into a decision tree. Crucially, they can compute the optimal policies for a range of complexity-performance trade-offs (different values of the regularization parameter α) in a single backward pass.

Comparison to Baselines: The authors compare their DPDT algorithm to several baselines, including optimal BnB solvers and greedy approaches like CART. They show that DPDT can find trees that are competitive with the optimal BnB solutions in terms of training accuracy, while being orders of magnitude faster. DPDT also outperforms CART in terms of generalization performance on unseen data.

Interpretability Analysis: The authors demonstrate that DPDT can provide a rich set of trees along the complexity-performance Pareto front, allowing users to select the tree that best suits their interpretability needs. This is in contrast to BnB approaches, which only return a single tree.

Overall, the article presents a novel and effective approach to decision tree learning that achieves a favorable trade-off between scalability, optimality, and interpretability.

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Viktiga insikter från

Interpretable Decision Tree Search as a Markov Decision Process

by Hector Kohle... på arxiv.org 04-02-2024

https://arxiv.org/pdf/2309.12701.pdf

Djupare frågor

How could the tests generating function be further improved to strike an even better balance between computational efficiency and solution quality

To further improve the tests generating function in DPDT, we can explore adaptive approaches that dynamically adjust the set of admissible tests based on the state of the MDP. One approach could be to incorporate a mechanism that prioritizes tests based on their information gain or discriminative power, similar to feature selection techniques. By dynamically selecting tests that are more likely to lead to significant improvements in the decision tree, we can strike a better balance between computational efficiency and solution quality. Additionally, incorporating domain-specific knowledge or constraints into the tests generating function can help tailor the search space to the specific characteristics of the dataset, further enhancing the quality of the generated decision trees.

What are the potential limitations of the MDP formulation in handling very large datasets or high-dimensional feature spaces

The MDP formulation may face limitations when handling very large datasets or high-dimensional feature spaces due to the exponential growth of the state space and action space. As the number of samples or features increases, the computational complexity of constructing and solving the MDP grows significantly, leading to scalability issues. Additionally, the memory requirements for storing the MDP states and transitions can become prohibitive for large datasets, potentially causing out-of-memory errors. Furthermore, the curse of dimensionality can impact the effectiveness of the MDP in high-dimensional feature spaces, as the number of possible tests and transitions increases exponentially with the number of features, making it challenging to explore the entire solution space efficiently.

Could the ideas presented in this work be extended to other types of interpretable models beyond decision trees, such as rule lists or decision sets

The ideas presented in this work can be extended to other types of interpretable models beyond decision trees, such as rule lists or decision sets. By formulating the learning process as a Markov Decision Problem (MDP) and incorporating a trade-off between complexity and performance, similar interpretability-focused models can be optimized. For rule lists, the MDP can be designed to sequentially add rules that maximize accuracy while minimizing complexity. Decision sets can be learned by defining actions that add or remove decision rules based on their impact on the model's performance and complexity. By adapting the MDP framework to these models, it is possible to achieve a similar balance between interpretability and accuracy in a variety of interpretable machine learning models.