Decision trees have gained popularity as interpretable surrogate models for learning-based control policies.

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Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is typically up to a decision maker to select one for implementation based on their subjective preferences. To reduce the cognitive load on the decision maker, previous work has introduced the Pareto pruning problem, where the goal is to compute a fixed-size subset of Pareto optimal solutions that best represent the full set, as evaluated by a given quality measure. Reframing Pareto pruning as a multiwinner voting problem, we conduct an axiomatic analysis of existing quality measures, uncovering several unintuitive behaviors. Motivated by these findings, we introduce a new measure, directed coverage. We also analyze the computational complexity of optimizing various quality measures, identifying previously unknown boundaries between tractable and intractable cases depending on the number and structure of the objectives. Finally, we present an experimental evaluation, demonstrating that the choice of quality measure has a decisive impact on the characteristics of the selected set of solutions and that our proposed measure performs competitively or even favorably across a range of settings.

We study the problem of learning a $n$-variables $k$-CNF formula $Φ$ from its i.i.d. uniform random solutions, which is equivalent to learning a Boolean Markov random field (MRF) with $k$-wise hard constraints. Revisiting Valiant's algorithm (Commun. ACM'84), we show that it can exactly learn (1) $k$-CNFs with bounded clause intersection size under Lovász local lemma type conditions, from $O(\log n)$ samples; and (2) random $k$-CNFs near the satisfiability threshold, from $\widetilde{O}(n^{\exp(-\sqrt{k})})$ samples. These results significantly improve the previous $O(n^k)$ sample complexity. We further establish new information-theoretic lower bounds on sample complexity for both exact and approximate learning from i.i.d. uniform random solutions.

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