Optimal Online Learning of Decision Trees with Thompson Sampling

Core Concepts

The core message of this article is to devise a new Monte Carlo Tree Search algorithm, called Thompson Sampling Decision Trees (TSDT), that can produce optimal Decision Trees in an online setting, and to provide strong convergence guarantees for this algorithm.

Abstract

The article introduces a new method for constructing optimal Decision Trees in an online setting, called Thompson Sampling Decision Trees (TSDT). The key insights are:

The authors formulate the problem of finding the optimal Decision Tree as a Markov Decision Process (MDP), where the optimal policy leads to the optimal Decision Tree.
They propose a novel Monte Carlo Tree Search (MCTS) algorithm, TSDT, that employs a Thompson Sampling policy to solve this MDP. TSDT is proven to converge almost surely to the optimal policy, and hence the optimal Decision Tree.
The authors also introduce a computationally more efficient variant called Fast-TSDT, which uses a simpler Backpropagation scheme.
Extensive experiments are conducted to validate the findings. TSDT and Fast-TSDT are shown to outperform existing greedy online Decision Tree methods, such as VFDT and EFDT, and also match or surpass the performance of recent batch optimal Decision Tree algorithms, such as DL8.5 and OSDT.
The article also discusses the limitations of the proposed methods, such as being restricted to categorical attributes, and outlines future work to address these limitations, including deriving finite-time convergence guarantees.

Stats

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Quotes

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Key Insights Distilled From

Online Learning of Decision Trees with Thompson Sampling

by Ayman Chaouk... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2404.06403.pdf

Deeper Inquiries

How can the proposed TSDT and Fast-TSDT algorithms be extended to handle numerical attributes

To extend the TSDT and Fast-TSDT algorithms to handle numerical attributes, we can utilize techniques such as binning or discretization. By discretizing the numerical attributes into categorical bins, we can treat them similarly to the existing categorical attributes. This process involves dividing the range of numerical values into intervals or bins and then assigning each value to the corresponding bin. This way, we can transform the numerical attributes into categorical ones, allowing us to apply the algorithms as they are designed for categorical attributes. Additionally, we can explore methods like decision tree ensembles, such as Random Forests or Gradient Boosted Trees, which naturally handle numerical attributes by considering multiple decision trees in the ensemble.

What are the theoretical limitations of the current convergence analysis, and how can they be addressed to obtain tighter finite-time guarantees

The current convergence analysis of TSDT and Fast-TSDT provides asymptotic guarantees, but obtaining tighter finite-time guarantees requires addressing several theoretical limitations. One limitation is the assumption of i.i.d. data, which may not hold in practice. Addressing this limitation involves exploring the impact of non-i.i.d. data on the convergence properties of the algorithms. Additionally, the analysis could be extended to consider the effect of noise or uncertainty in the data on the convergence rates. Another limitation is the assumption of a fixed horizon, which may not be realistic in dynamic environments. Addressing this limitation involves investigating the algorithms' performance under varying time horizons or adapting the algorithms to handle changing horizons dynamically. By addressing these limitations and incorporating them into the theoretical analysis, we can obtain tighter finite-time guarantees for the algorithms.

What other MCTS policies, such as UCB or ε-greedy, could be explored in the context of optimal online Decision Tree construction, and how would their performance and theoretical properties compare to Thompson Sampling

Exploring other MCTS policies, such as UCB or ε-greedy, in the context of optimal online Decision Tree construction offers opportunities for comparison and improvement. UCB, known for balancing exploration and exploitation, could provide a more systematic approach to decision-making during tree construction. By incorporating UCB, the algorithm could prioritize exploring less explored branches, potentially leading to more optimal decision trees. On the other hand, ε-greedy, which balances exploration and exploitation by randomly selecting actions with a certain probability, could introduce a level of randomness that may help in avoiding local optima. Comparing the performance and theoretical properties of these policies with Thompson Sampling could provide insights into the strengths and weaknesses of each approach in the context of online Decision Tree construction.