An Exhaustive DPLL Approach to Model Counting over Integer Linear Constraints with Simplification Techniques

Linear constraints are one of the most fundamental constraints in fields such as computer science, operations research and optimization. Many applications reduce to the task of model counting over integer linear constraints (MCILC). In this paper, we design an exact approach to MCILC based on an exhaustive DPLL architecture. To improve the efficiency, we integrate several effective simplification techniques from mixed integer programming into the architecture. We compare our approach to state-of-the-art MCILC counters and propositional model counters on 2840 random and 4131 application benchmarks. Experimental results show that our approach significantly outperforms all exact methods in random benchmarks solving 1718 instances while the state-of-the-art approach only computes 1470 instances. In addition, our approach is the only approach to solve all 4131 application instances.

Interactive Search Based on Deep Reinforcement Learning

With the continuous development of machine learning technology, major e-commerce platforms have launched recommendation systems based on it to serve a large number of customers with different needs more efficiently. Compared with traditional supervised learning, reinforcement learning can better capture the user's state transition in the decision-making process, and consider a series of user actions, not just the static characteristics of the user at a certain moment. In theory, it will have a long-term perspective, producing a more effective recommendation. The special requirements of reinforcement learning for data make it need to rely on an offline virtual system for training. Our project mainly establishes a virtual user environment for offline training. At the same time, we tried to improve a reinforcement learning algorithm based on bi-clustering to expand the action space and recommended path space of the recommendation agent.