Breiman meets Bellman: Non-Greedy Decision Trees with MDPs

• URL: http://arxiv.org/abs/2309.12701v5
• Date: Sun, 01 Jun 2025 16:37:37 GMT
• Title: Breiman meets Bellman: Non-Greedy Decision Trees with MDPs
• Authors: Hector Kohler, Riad Akrour, Philippe Preux,
• Abstract summary: We present Dynamic Programming Decision Trees (DPDT), a framework that bridges the gap between greedy and optimal approaches.<n>DPDT relies on a Markov Decision Process formulation combined with split generation to construct near-optimal decision trees.<n>Our empirical study shows that DPDT achieves near-optimal loss with orders of magnitude fewer operations than existing optimal solvers.
• Score: 8.530182510074983
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In supervised learning, decision trees are valued for their interpretability and performance. While greedy decision tree algorithms like CART remain widely used due to their computational efficiency, they often produce sub-optimal solutions with respect to a regularized training loss. Conversely, optimal decision tree methods can find better solutions but are computationally intensive and typically limited to shallow trees or binary features. We present Dynamic Programming Decision Trees (DPDT), a framework that bridges the gap between greedy and optimal approaches. DPDT relies on a Markov Decision Process formulation combined with heuristic split generation to construct near-optimal decision trees with significantly reduced computational complexity. Our approach dynamically limits the set of admissible splits at each node while directly optimizing the tree regularized training loss. Theoretical analysis demonstrates that DPDT can minimize regularized training losses at least as well as CART. Our empirical study shows on multiple datasets that DPDT achieves near-optimal loss with orders of magnitude fewer operations than existing optimal solvers. More importantly, extensive benchmarking suggests statistically significant improvements of DPDT over both CART and optimal decision trees in terms of generalization to unseen data. We demonstrate DPDT practicality through applications to boosting, where it consistently outperforms baselines. Our framework provides a promising direction for developing efficient, near-optimal decision tree algorithms that scale to practical applications.

Related papers

• Learning Deep Tree-based Retriever for Efficient Recommendation: Theory and Method [76.31185707649227]
  We propose a Deep Tree-based Retriever (DTR) for efficient recommendation. DTR frames the training task as a softmax-based multi-class classification over tree nodes at the same level. To mitigate the suboptimality induced by the labeling of non-leaf nodes, we propose a rectification method for the loss function.
  arXiv  Detail & Related papers  (2024-08-21T05:09:53Z)
• An Unsupervised Learning Framework Combined with Heuristics for the Maximum Minimal Cut Problem [5.092968949752308]
  This work proposes an unsupervised learning framework combined with Maximums for MMCP. A crucial observation is that each solution corresponds to at least one spanning tree. We conduct extensive experiments to evaluate our framework and give a specific application.
  arXiv  Detail & Related papers  (2024-08-16T02:07:34Z)
• Learning a Decision Tree Algorithm with Transformers [75.96920867382859]
  We introduce MetaTree, a transformer-based model trained via meta-learning to directly produce strong decision trees. We fit both greedy decision trees and globally optimized decision trees on a large number of datasets, and train MetaTree to produce only the trees that achieve strong generalization performance.
  arXiv  Detail & Related papers  (2024-02-06T07:40:53Z)
• Online POMDP Planning with Anytime Deterministic Optimality Guarantees [9.444784653236157]
  We derive a deterministic relationship for discrete POMDPs between an approximated and the optimal solution. We show that our derivations provide an avenue for a new set of algorithms and can be attached to existing algorithms.
  arXiv  Detail & Related papers  (2023-10-03T04:40:38Z)
• TreeDQN: Learning to minimize Branch-and-Bound tree [78.52895577861327]
  Branch-and-Bound is a convenient approach to solving optimization tasks in the form of Mixed Linear Programs. The efficiency of the solver depends on the branchning used to select a variable for splitting. We propose a reinforcement learning method that can efficiently learn the branching.
  arXiv  Detail & Related papers  (2023-06-09T14:01:26Z)
• Optimal Decision Tree Policies for Markov Decision Processes [7.995360025953931]
  We study the optimization of size-limited decision trees for Markov Decision Processes (MPDs) We show that this is due to an inherent shortcoming of imitation learning, namely that complex policies cannot be represented using size-limited trees. While there is generally a trade-off between the performance and interpretability of machine learning models, we find that OMDTs limited to a depth of 3 often perform close to the optimal limit.
  arXiv  Detail & Related papers  (2023-01-30T18:51:02Z)
• Quant-BnB: A Scalable Branch-and-Bound Method for Optimal Decision Trees with Continuous Features [5.663538370244174]
  We present a new discrete optimization method based on branch-and-bound (BnB) to obtain optimal decision trees. Our proposed algorithm Quant-BnB shows significant speedups compared to existing approaches for shallow optimal trees on various real datasets.
  arXiv  Detail & Related papers  (2022-06-23T17:19:29Z)
• bsnsing: A decision tree induction method based on recursive optimal boolean rule composition [2.28438857884398]
  This paper proposes a new mixed-integer programming (MIP) formulation to optimize split rule selection in the decision tree induction process. It develops an efficient search solver that is able to solve practical instances faster than commercial solvers.
  arXiv  Detail & Related papers  (2022-05-30T17:13:57Z)
• Optimal Decision Diagrams for Classification [68.72078059880018]
  We study the training of optimal decision diagrams from a mathematical programming perspective. We introduce a novel mixed-integer linear programming model for training. We show how this model can be easily extended for fairness, parsimony, and stability notions.
  arXiv  Detail & Related papers  (2022-05-28T18:31:23Z)
• Reinforcement Learning for Branch-and-Bound Optimisation using Retrospective Trajectories [72.15369769265398]
  Machine learning has emerged as a promising paradigm for branching. We propose retro branching; a simple yet effective approach to RL for branching. We outperform the current state-of-the-art RL branching algorithm by 3-5x and come within 20% of the best IL method's performance on MILPs with 500 constraints and 1000 variables.
  arXiv  Detail & Related papers  (2022-05-28T06:08:07Z)
• Learning Proximal Operators to Discover Multiple Optima [66.98045013486794]
  We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
  arXiv  Detail & Related papers  (2022-01-28T05:53:28Z)
• What's Wrong with Deep Learning in Tree Search for Combinatorial Optimization [8.879790406465556]
  We present an open-source benchmark suite for the NP-hard Maximum Independent Set problem, in both its weighted and unweighted variants. We also conduct an in-depth analysis of the popular guided tree search algorithm by Li et al. [NeurIPS 2018], testing various configurations on small and large synthetic and real-world graphs. We show that the graph convolution network used in the tree search does not learn a meaningful representation of the solution structure, and can in fact be replaced by random values.
  arXiv  Detail & Related papers  (2022-01-25T17:37:34Z)
• Robust Optimal Classification Trees Against Adversarial Examples [5.254093731341154]
  We propose a collection of methods to train decision trees that are optimally robust against user-specified attack models. We show that the min-max optimization problem that arises in adversarial learning can be solved using a single minimization formulation. We also present a method that determines the upper bound on adversarial accuracy for any model using bipartite matching.
  arXiv  Detail & Related papers  (2021-09-08T18:10:49Z)
• Modularity in Reinforcement Learning via Algorithmic Independence in Credit Assignment [79.5678820246642]
  We show that certain action-value methods are more sample efficient than policy-gradient methods on transfer problems that require only sparse changes to a sequence of previously optimal decisions. We generalize the recently proposed societal decision-making framework as a more granular formalism than the Markov decision process.
  arXiv  Detail & Related papers  (2021-06-28T21:29:13Z)
• Learning to Schedule Heuristics in Branch-and-Bound [25.79025327341732]
  Real-world applications typically require finding good solutions early in the search to enable fast decision-making. We propose the first data-driven framework for schedulings in an exact MIP solver. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances.
  arXiv  Detail & Related papers  (2021-03-18T14:49:52Z)
• Online Model Selection for Reinforcement Learning with Function Approximation [50.008542459050155]
  We present a meta-algorithm that adapts to the optimal complexity with $tildeO(L5/6 T2/3)$ regret. We also show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds.
  arXiv  Detail & Related papers  (2020-11-19T10:00:54Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• MurTree: Optimal Classification Trees via Dynamic Programming and Search [61.817059565926336]
  We present a novel algorithm for learning optimal classification trees based on dynamic programming and search. Our approach uses only a fraction of the time required by the state-of-the-art and can handle datasets with tens of thousands of instances.
  arXiv  Detail & Related papers  (2020-07-24T17:06:55Z)
• Generalized and Scalable Optimal Sparse Decision Trees [56.35541305670828]
  We present techniques that produce optimal decision trees over a variety of objectives. We also introduce a scalable algorithm that produces provably optimal results in the presence of continuous variables.
  arXiv  Detail & Related papers  (2020-06-15T19:00:11Z)
• ENTMOOT: A Framework for Optimization over Ensemble Tree Models [57.98561336670884]
  ENTMOOT is a framework for integrating tree models into larger optimization problems. We show how ENTMOOT allows a simple integration of tree models into decision-making and black-box optimization.
  arXiv  Detail & Related papers  (2020-03-10T14:34:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.