title: Optimal decision trees via search: A reinforcement learning framework

authors: Chaouki, Ayman

subjects: Decision Trees

abstract: Decision Trees are one of the most popular models in Machine Learning because of their interpretability, which is especially noticeable for Decision Trees with few splits (or decision rules), a property that is called sparsity. Interpretable models are highly valued in domains where decisions carry substantial ramifications such as health-care and the criminal justice system. For this reason, seeking optimal sparse Decision Trees constitutes a fundamental problem in Interpretable Machine Learning, and a large research effort has been devoted to solving this problem.

Due to the NP-Hard difficulty of the problem, greedy heuristic methods such as C4.5 and CART have been favoured historically, and while fast and scalable, these methods remain unsatisfactory because they forgo the sparsity portion of the problem. In fact, they often lead to suboptimal and overly complex Decision Trees. Nevertheless, many algorithms have been developed in the literature to address the sparsity problem, with recent breakthroughs leveraging Dynamic Programming (DP) and Branch & Bound (B&B) techniques, and causing a paradigm shift from traditional Mathematical Programming to search algorithms. However, most of the proposed DP and B&B methods follow a Depth-First-Search (DFS) strategy, which, while attractive due to its storage-economy capacity, is inefficient because of its uninformative nature. Moreover, DFS necessitates the definition of a maximum depth hyperparameter a priori, and its inefficiency becomes a limiting factor when considering large maximum depths. These concerns were partially addressed with Best-First-Search (BFS) strategies. BFS is appealing because it prunes the search space more aggressively without losing the optimality guarantee, thus enabling it to find the optimal solution faster than DFS. Moreover, BFS does not necessitate fixing a maximum depth hyperparameter, it can run on infinite depth, which is an important advantage that allows practitioners to focus tuning efforts on other hyperparameters. However, these advantages come at the expense of higher memory consumption than DFS. To alleviate this issue, the search strategies of BFS methods have to be formulated as efficiently as possible, in other words, they need to find the optimal solution as quickly as possible. The reason being to tip the balance of their advantages-drawbacks more towards their advantages, outweighing their high memory consumption issue.

The current BFS methods can be improved substantially by reconsidering the sparsity problem under a framework that benefits from its structural properties. Our main contribution in this thesis addresses this concern within a Reinforcement Learning framework. Our BFS algorithm, Branches, benefits from an AO*-type search strategy, which, coupled with our pruning bound we call Purification Bound and several other heuristic considerations, focuses the search on relevant regions of the search space while maintaining the optimality guarantee. This enables Branches to find optimal sparse Decision Trees faster than the state of the art, and as a result alleviate the memory burden that weighs on BFS approaches. We analyse the computational complexity of Branches theoretically by deriving an upper bound on the number of branch evaluations it performs before terminating, and we show this result to be superior to similar analyses from the literature. These findings are further validated through a series of extensive experiments showing Branches to significantly advance the state of the art in terms of number of iterations, runtime, anytime behaviour and scalability potential. This work lays the foundations for future work that can further improve the scalability of these methods.

In addition to this work, we also study the online setting where a data stream is observed rather than a fixed dataset. Unlike the batch setting, the literature on optimal sparse Decision Trees in is scarce for Online Learning. Most approaches adapt greedy heuristics to handling data streams through statistical estimates, hence inheriting their suboptimality issues. On this front, we develop three Monte Carlo Tree Search (MCTS) algorithms with asymptotic optimality guarantees, and we show that they can successfully retrieve the optimal solution in situations where the state of the art methods are practically guaranteed to fail. Furthermore, we adapt Branches to the online setting inducing Online-Branches, an algorithm that satisfies finite-time optimality guarantees rather than asymptotic ones. Our experiments show Online-Branches to outperform our previously developed MCTS methods. Our work on the online setting has the potential to draw more research attention to the problem of seeking optimal sparse Decision Trees when given a data stream. It also lays a solid foundation for these future works through several discussions about the potential issues that arise due to the hypotheses of Online Learning and our proposed solutions.

text: Optimal decision trees via search: A reinforcement learning framework Decision Trees are one of the most popular models in Machine Learning because of their interpretability, which is especially noticeable for Decision Trees with few splits (or decision rules), a property that is called sparsity. Interpretable models are highly valued in domains where decisions carry substantial ramifications such as health-care and the criminal justice system. For this reason, seeking optimal sparse Decision Trees constitutes a fundamental problem in Interpretable Machine Learning, and a large research effort has been devoted to solving this problem.

Due to the NP-Hard difficulty of the problem, greedy heuristic methods such as C4.5 and CART have been favoured historically, and while fast and scalable, these methods remain unsatisfactory because they forgo the sparsity portion of the problem. In fact, they often lead to suboptimal and overly complex Decision Trees. Nevertheless, many algorithms have been developed in the literature to address the sparsity problem, with recent breakthroughs leveraging Dynamic Programming (DP) and Branch & Bound (B&B) techniques, and causing a paradigm shift from traditional Mathematical Programming to search algorithms. However, most of the proposed DP and B&B methods follow a Depth-First-Search (DFS) strategy, which, while attractive due to its storage-economy capacity, is inefficient because of its uninformative nature. Moreover, DFS necessitates the definition of a maximum depth hyperparameter a priori, and its inefficiency becomes a limiting factor when considering large maximum depths. These concerns were partially addressed with Best-First-Search (BFS) strategies. BFS is appealing because it prunes the search space more aggressively without losing the optimality guarantee, thus enabling it to find the optimal solution faster than DFS. Moreover, BFS does not necessitate fixing a maximum depth hyperparameter, it can run on infinite depth, which is an important advantage that allows practitioners to focus tuning efforts on other hyperparameters. However, these advantages come at the expense of higher memory consumption than DFS. To alleviate this issue, the search strategies of BFS methods have to be formulated as efficiently as possible, in other words, they need to find the optimal solution as quickly as possible. The reason being to tip the balance of their advantages-drawbacks more towards their advantages, outweighing their high memory consumption issue.

The current BFS methods can be improved substantially by reconsidering the sparsity problem under a framework that benefits from its structural properties. Our main contribution in this thesis addresses this concern within a Reinforcement Learning framework. Our BFS algorithm, Branches, benefits from an AO*-type search strategy, which, coupled with our pruning bound we call Purification Bound and several other heuristic considerations, focuses the search on relevant regions of the search space while maintaining the optimality guarantee. This enables Branches to find optimal sparse Decision Trees faster than the state of the art, and as a result alleviate the memory burden that weighs on BFS approaches. We analyse the computational complexity of Branches theoretically by deriving an upper bound on the number of branch evaluations it performs before terminating, and we show this result to be superior to similar analyses from the literature. These findings are further validated through a series of extensive experiments showing Branches to significantly advance the state of the art in terms of number of iterations, runtime, anytime behaviour and scalability potential. This work lays the foundations for future work that can further improve the scalability of these methods.

In addition to this work, we also study the online setting where a data stream is observed rather than a fixed dataset. Unlike the batch setting, the literature on optimal sparse Decision Trees in is scarce for Online Learning. Most approaches adapt greedy heuristics to handling data streams through statistical estimates, hence inheriting their suboptimality issues. On this front, we develop three Monte Carlo Tree Search (MCTS) algorithms with asymptotic optimality guarantees, and we show that they can successfully retrieve the optimal solution in situations where the state of the art methods are practically guaranteed to fail. Furthermore, we adapt Branches to the online setting inducing Online-Branches, an algorithm that satisfies finite-time optimality guarantees rather than asymptotic ones. Our experiments show Online-Branches to outperform our previously developed MCTS methods. Our work on the online setting has the potential to draw more research attention to the problem of seeking optimal sparse Decision Trees when given a data stream. It also lays a solid foundation for these future works through several discussions about the potential issues that arise due to the hypotheses of Online Learning and our proposed solutions.

year: 2024

title: Food rescue in New Zealand:  A sector in transformation

authors: Mulder, Megan

abstract: The COVID-19 pandemic significantly impacted New Zealand’s food rescue sector, exposing vulnerabilities and spurring opportunities. Through 18 qualitative interviews and secondary data, this report explores the post-pandemic changes in the sector. First, the food rescue ecosystem has been significantly reshaped through the emergence of new actors and an increase in actors creating new dynamics in the sector. Second, with the shifts in funding post-pandemic, organisations have been exploring new ways of generating revenue but are also struggling with infrastructural and resource issues. Third, to meet community needs, food rescue organisations have cultivated capacities to innovate new practices. Fourth, the sector is showing clear signs of professionalisation including the standardisation and normalisation of practices, the creation of frameworks and the emergence of clearer boundaries around the field. And fifth, our interviewees are raising questions about the purpose and raison d’être of the sector. 
Those changes highlight three main challenges for the sector. First, the sector is facing a number of paradoxical tensions: collaborating vs competing, efficiency vs relational focus, standardising vs improvising, food insecurity vs food waste and acting locally vs nationally. Although those tensions are not all entirely new, they have become increasingly salient post-COVID. Another challenge is the need for organisations to adapt to the constant changes and build resilience. And the third challenge requires thinking beyond the sector to address the systemic issues of food waste and food insecurity. Recognising and addressing those challenges is necessary for the food rescue to continue to develop and adapt but also to remain societally relevant.

text: Food rescue in New Zealand:  A sector in transformation The COVID-19 pandemic significantly impacted New Zealand’s food rescue sector, exposing vulnerabilities and spurring opportunities. Through 18 qualitative interviews and secondary data, this report explores the post-pandemic changes in the sector. First, the food rescue ecosystem has been significantly reshaped through the emergence of new actors and an increase in actors creating new dynamics in the sector. Second, with the shifts in funding post-pandemic, organisations have been exploring new ways of generating revenue but are also struggling with infrastructural and resource issues. Third, to meet community needs, food rescue organisations have cultivated capacities to innovate new practices. Fourth, the sector is showing clear signs of professionalisation including the standardisation and normalisation of practices, the creation of frameworks and the emergence of clearer boundaries around the field. And fifth, our interviewees are raising questions about the purpose and raison d’être of the sector. 
Those changes highlight three main challenges for the sector. First, the sector is facing a number of paradoxical tensions: collaborating vs competing, efficiency vs relational focus, standardising vs improvising, food insecurity vs food waste and acting locally vs nationally. Although those tensions are not all entirely new, they have become increasingly salient post-COVID. Another challenge is the need for organisations to adapt to the constant changes and build resilience. And the third challenge requires thinking beyond the sector to address the systemic issues of food waste and food insecurity. Recognising and addressing those challenges is necessary for the food rescue to continue to develop and adapt but also to remain societally relevant.

year: 2025

title: Introduction: Recognition, redistribution and reconciliation in postcolonial settler societies

authors: van Meijl, Toon

subjects: multiculturalism

abstract: Various questions are addressed regarding recognition of special rights for indigenous minorities in postcolonial nation-states, redistributing resources to redress longstanding indigenous grievances about the history of colonial dispossession and strategy of reconciliation between the immigrant majority of settlers and their descendants against a backdrop of multiculturalism.

text: Introduction: Recognition, redistribution and reconciliation in postcolonial settler societies Various questions are addressed regarding recognition of special rights for indigenous minorities in postcolonial nation-states, redistributing resources to redress longstanding indigenous grievances about the history of colonial dispossession and strategy of reconciliation between the immigrant majority of settlers and their descendants against a backdrop of multiculturalism.

year: 2003-09-01