Model-based offline reinforcement learning (RL) is a compelling approach that addresses the challenge of learning from limited, static data by generating imaginary trajectories using learned models. However, it falls short in solving long-horizon tasks due to high bias in value estimation from model rollouts. In this paper, we introduce a novel model-based offline RL method, Lower Expectile Q-learning (LEQ), which enhances long-horizon task performance by mitigating the high bias in model-based value estimation via expectile regression of $\lambda$-returns. Our empirical results show that LEQ significantly outperforms previous model-based offline RL methods on long-horizon tasks, such as the D4RL AntMaze tasks, matching or surpassing the performance of model-free approaches. Our experiments demonstrate that expectile regression, $\lambda$-returns, and critic training on offline data are all crucial for addressing long-horizon tasks. Additionally, LEQ achieves performance comparable to the state-of-the-art model-based and model-free offline RL methods on the NeoRL benchmark and the D4RL MuJoCo Gym tasks.

Program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values over multiple examples, such as intervals. To overcome this limitation, we introduce an inductive logic programming approach which combines relational learning with numerical reasoning. Our approach, which we call NUMSYNTH, uses satisfiability modulo theories solvers to efficiently learn programs with numerical values. Our approach can identify numerical values in linear arithmetic fragments, such as real difference logic, and from infinite domains, such as real numbers or integers. Our experiments on four diverse domains, including game playing and program synthesis, show that our approach can (i) learn programs with numerical values from linear arithmetical reasoning, and (ii) outperform existing approaches in terms of predictive accuracies and learning times.