Reinforcement Learning-Based Adaptive Reset Policy for Improving CDCL SAT Solver Performance

Core Concepts

Reinforcement learning-based adaptive reset policies can dynamically and profitably adapt the reset frequency for any given input instance, outperforming traditional restart and fixed reset policies.

Abstract

The paper proposes reinforcement learning (RL) based adaptive reset policies for Conflict-Driven Clause Learning (CDCL) SAT solvers. The key ideas are: Modeling the problem of whether to reset or restart as a multi-armed bandit (MAB) problem, and solving it using the Upper Confidence Bound (UCB) method and Thompson sampling. This allows the solver to adaptively decide when to reset based on the observed successes and failures from previous resets/restarts. Introducing the concept of "partial reset", where the order of top activity variables is preserved across reset boundaries, to retain some "locality" information of the branching heuristic. Extensive empirical evaluation of the RL-based reset policies on three benchmark sets (SAT Competition Main Track 2022/2023 and Satcoin) over four state-of-the-art CDCL solvers (CaDiCaL, SBVA_Cadical, Kissat, MapleSAT). The results show that the RL-based reset versions outperform or match the performance of the baseline solvers on the evaluated benchmarks.

Stats

The paper reports the number of instances solved by the baseline and RL-based reset versions of the CDCL solvers on the SAT Competition Main Track 2022, SAT Competition Main Track 2023, and Satcoin benchmarks.

Quotes

"Restart policies are an important and widely studied class of techniques used in state-of-the-art Conflict-Driven Clause Learning (CDCL) Boolean SAT solvers, wherein some parts of the state of solvers is erased at certain intervals during the run of the solver." "To enable the solver to search possibly "distant" parts of the assignment tree, we study the effect of resets, a variant of restarts which not only erases the assignment trail, but also randomizes the activity scores of the variables of the input formula after reset, thus potentially enabling a better global exploration of the search space."

Key Insights Distilled From

A Reinforcement Learning based Reset Policy for CDCL SAT Solvers

by Chunxiao Li,... at arxiv.org 04-08-2024

https://arxiv.org/pdf/2404.03753.pdf

Deeper Inquiries

How can the RL-based reset policies be further improved to achieve even better performance on a wider range of benchmark suites

To further improve the performance of RL-based reset policies on a wider range of benchmark suites, several enhancements can be considered: Dynamic Exploration-Exploitation Balance: Implementing more sophisticated exploration-exploitation strategies within the RL framework can help the solver adapt better to different instances. Techniques like epsilon-greedy with a decaying epsilon or using more advanced exploration algorithms like Upper Confidence Bound (UCB) can enhance the solver's ability to explore the search space effectively. Feature Engineering: Introducing more informative features that capture the characteristics of the input instances can improve the learning process. Features related to the structure of the formula, variable interactions, or clause properties can provide valuable insights for the RL model to make better decisions. Ensemble Methods: Combining multiple RL models or incorporating ensemble learning techniques can leverage the strengths of different models and enhance the overall performance. By aggregating the decisions of multiple models, the solver can benefit from diverse perspectives and improve decision-making. Transfer Learning: Utilizing transfer learning techniques to transfer knowledge gained from solving one set of benchmarks to another can help the RL model generalize better across different types of instances. By leveraging insights from previously solved instances, the solver can adapt more efficiently to new challenges.

What are the potential drawbacks or limitations of the proposed RL-based reset policies, and how can they be addressed

While RL-based reset policies offer significant advantages, there are potential drawbacks and limitations that need to be addressed: Overfitting: The RL model may overfit to specific patterns in the training data, leading to suboptimal performance on unseen instances. Regularization techniques and diverse training data can help mitigate overfitting and improve generalization. Computational Complexity: RL-based approaches can be computationally intensive, especially when dealing with large-scale benchmarks. Optimizing the training process, utilizing parallel computing, and efficient algorithms can help reduce computational overhead. Hyperparameter Tuning: The performance of RL models heavily depends on hyperparameters such as learning rates, exploration rates, and decay factors. Fine-tuning these hyperparameters through systematic experimentation and grid search can enhance the effectiveness of the RL-based reset policies. Robustness to Noisy Data: RL models may be sensitive to noisy or inconsistent data, which can impact their decision-making process. Preprocessing techniques, data cleaning, and robust reward mechanisms can help the model handle noisy inputs more effectively.

Can the ideas of adaptive reset policies be extended to other heuristics in CDCL solvers, such as branching or clause deletion, to achieve more holistic performance improvements

The concept of adaptive reset policies can indeed be extended to other heuristics in CDCL solvers, such as branching or clause deletion, to achieve more holistic performance improvements: Adaptive Branching Heuristics: By incorporating RL-based adaptive strategies for selecting branching variables, the solver can dynamically adjust its branching decisions based on the characteristics of the input instance. This can lead to more efficient exploration of the search space and faster convergence to solutions. Dynamic Clause Deletion Policies: Implementing RL-based techniques to adaptively manage the deletion of learned clauses can optimize the trade-off between memory usage and search efficiency. The solver can learn when to retain or discard clauses based on their relevance to the current search state, improving overall performance. Combined Adaptive Strategies: Integrating adaptive reset, branching, and clause deletion policies within a unified framework can create a synergistic effect, where the solver dynamically adjusts multiple heuristics based on the evolving search landscape. This comprehensive approach can lead to significant performance gains across a wide range of problem instances.