Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. To address this gap, we use domain expert annotation to curate a high-quality synthetic training dataset for this task. We show the value of this data by using it to iteratively finetune Llama-2 (70B) to create MATHWELL, a K-8 word problem generator. Domain experts find MATHWELL has a 40% higher share of problems that have executable solutions and meet all criteria than existing open-source models, with 74% of its problems with executable solutions being solvable, accurate, and appropriate. MATHWELL achieves 94.9% of GPT-4 Turbo's performance on this task while outputting problems written at a more appropriate reading level for K-8 students. MATHWELL's performance despite being trained by finetuning only highlights the quality of our synthetic data for training age-appropriate word problem generators. We release our model, data, and annotations.

This paper introduces two new frameworks for learning action models for planning. In the mistake-bounded planning framework, the learner has access to a planner for the given model representation, a simulator, and a planning problem generator, and aims to learn a model with at most a polynomial number of faulty plans. In the planned exploration framework, the learner does not have access to a problem generator and must instead design its own problems, plan for them, and converge with at most a polynomial number of planning attempts. The paper reduces learning in these frameworks to concept learning with one-sided error and provides algorithms for successful learning in both frameworks. A specific family of hypothesis spaces is shown to be efficiently learnable in both the frameworks.

Sequential transfer optimization (STO), which aims to improve the optimization performance on a task of interest by exploiting the knowledge captured from several previously-solved optimization tasks stored in a database, has been gaining increasing research attention over the years. However, despite the remarkable advances in algorithm design, the development of a systematic benchmark suite for comprehensive comparisons of STO algorithms received far less attention. Existing test problems are either simply generated by assembling other benchmark functions or extended from specific practical problems with limited scalability. The relationships between the optimal solutions of the source and target tasks in these problems are also often manually configured, limiting their ability to model different similarity relationships presented in real-world problems. Consequently, the good performance achieved by an algorithm on these problems might be biased and hard to be generalized to other problems. In light of the above, in this study, we first introduce four concepts for characterizing STO problems and present an important problem feature, namely similarity distribution, which quantitatively delineates the relationship between the optima of the source and target tasks. Then, we present the general design guidelines of STO problems and a particular STO problem generator with good scalability. Specifically, the similarity distribution of a problem can be easily customized, enabling a continuous spectrum of representation of the diverse similarity relationships of real-world problems. Lastly, a benchmark suite with 12 STO problems featured by a variety of customized similarity relationships is developed using the proposed generator. The source code of the problem generator is available at https://github.com/XmingHsueh/STOP-G.

This paper introduces two new frameworks for learning action models for planning. In the mistake-bounded planning framework, the learner has access to a planner for the given model representation, a simulator, and a planning problem generator, and aims to learn a model with at most a polynomial number of faulty plans. In the planned exploration framework, the learner does not have access to a problem generator and must instead design its own problems, plan for them, and converge with at most a polynomial number of planning attempts. The paper reduces learning in these frameworks to concept learning with one-sided error and provides algorithms for successful learning in both frameworks. A specific family of hypothesis spaces is shown to be efficiently learnable in both the frameworks.

This paper introduces two new frameworks for learning action models for planning. In the mistake-bounded planning framework, the learner has access to a planner for the given model representation, a simulator, and a planning problem generator, and aims to learn a model with at most a polynomial number of faulty plans. In the planned exploration framework, the learner does not have access to a problem generator and must instead design its own problems, plan for them, and converge with at most a polynomial number of planning attempts. The paper reduces learning in these frameworks to concept learning with one-sided error and provides algorithms for successful learning in both frameworks. A specific family of hypothesis spaces is shown to be efficiently learnable in both the frameworks.

This paper introduces two new frameworks for learning action models for planning. In the mistake-bounded planning framework, the learner has access to a planner for the given model representation, a simulator, and a planning problem generator, and aims to learn a model with at most a polynomial number of faulty plans. In the planned exploration framework, the learner does not have access to a problem generator and must instead design its own problems, plan for them, and converge with at most a polynomial number of planning attempts. The paper reduces learning in these frameworks to concept learning with one-sided error and provides algorithms for successful learning in both frameworks. A specific family of hypothesis spaces is shown to be efficiently learnable in both the frameworks.

Domain-specific features are important in representing problem structure throughout machine learning and decision-theoretic planning. In planning, once state features are provided, domain-independent algorithms such as approximate value iteration can learn weighted combinations of those features that often perform well as heuristic estimates of state value (e.g., distance to the goal). Successful applications in real-world domains often require features crafted by human experts. Here, we propose automatic processes for learning useful domain-specific feature sets with little or no human intervention. Our methods select and add features that describe state-space regions of high inconsistency in the Bellman equation (statewise Bellman error) during approximate value iteration. Our method can be applied using any real-valued-feature hypothesis space and corresponding learning method for selecting features from training sets of state-value pairs. We evaluate the method with hypothesis spaces defined by both relational and propositional feature languages, using nine probabilistic planning domains. We show that approximate value iteration using a relational feature space performs at the state-of-the-art in domain-independent stochastic relational planning. Our method provides the first domain-independent approach that plays Tetris successfully (without human-engineered features).