本研究对比极小极大博弈中的深度优先算法 AB 和最佳优先算法 SSS,理论证明 SSS 实为 AB 的特例,实证推翻了 SSS 复杂、耗内存且更高效的普遍观点。
摘要:
搜索算法通常根据其节点扩展策略进行分类。一种选择是深度优先策略,这是一种简单的回溯策略,按照生成后继节点的顺序遍历搜索空间。另一种选择是最佳优先策略,其设计旨在使利用特定领域的启发式信息成为可能。通过优先探索搜索空间中有前景的部分,最佳优先算法通常比深度优先算法更高效。在诸如国际象棋和跳棋等极小极大博弈程序中,搜索的效率至关重要。鉴于最佳优先算法在其他领域的成功,人们期望它们也能用于极小极大博弈。然而,所有高性能的博弈程序都基于深度优先算法。本研究深入探讨了深度优先算法 AB 和最佳优先算法 SSS。关于这些算法的普遍观点是,SSS 提供了更高效搜索的潜力,但其复杂的公式表述和指数级的内存需求使其不切实际。这项工作的理论部分表明,这两种算法之间存在着惊人直接的联系——就所有实际目的而言,SSS 是 AB 的一个特例。随后的实证证据证明关于 SSS 的普遍观点是错误的:它并不是一个复杂的算法,它不需要太多内存,而且也不比深度优先搜索更高效。
英文摘要:
Search algorithms are often categorized by their node expansion strategy. One option is the depth-first strategy, a simple backtracking strategy that traverses the search space in the order in which successor nodes are generated. An alternative is the best-first strategy, which was designed to make it possible to use domain-specific heuristic information. By exploring promising parts of the search space first, best-first algorithms are usually more efficient than depth-first algorithms.
In programs that play minimax games such as chess and checkers, the efficiency of the search is of crucial importance. Given the success of best-first algorithms in other domains, one would expect them to be used for minimax games too. However, all high-performance game-playing programs are based on a depth-first algorithm.
This study takes a closer look at a depth-first algorithm, AB, and a best-first algorithm, SSS. The prevailing opinion on these algorithms is that SSS offers the potential for a more efficient search, but that its complicated formulation and exponential memory requirements render it impractical. The theoretical part of this work shows that there is a surprisingly straightforward link between the two algorithms -- for all practical purposes, SSS is a special case of AB. Subsequent empirical evidence proves the prevailing opinion on SSS to be wrong: it is not a complicated algorithm, it does not need too much memory, and it is also not more efficient than depth-first search.
ReSearch: Learning to Reason with Search for LLMs via Reinforcement Learning
Baichuan Inc.(北川公司);University of Chinese Academy of Sciences(中国科学院大学);Tongji University(同济大学);The University of Edinburgh(爱丁堡大学);Zhejiang University(浙江大学)
ReSearch 提出通过强化学习训练 LLMs 将搜索操作融入推理链,无需监督推理步骤,在 Qwen2.5 系列模型上训练后展现出跨基准的强泛化能力,并自然涌现反思与自我纠错能力。
DEEPMED Search: An Open-Source Agentic Platform for Medical Deep Research with Introspective Verification
School of Computer Science and Software Engineering, Shanghai University(上海大学计算机科学与软件工程学院);Department of Computer Science and Engineering, Shanghai Jiao Tong University(上海交通大学计算机科学与工程系)
Automating Bibliometric Analysis with Sentence Transformers and Retrieval-Augmented Generation (RAG): A Pilot Study in Semantic and Contextual Search for Customized Literature Characterization for High-Impact Urban Research
Oak Ridge National Laboratory(橡树岭国家实验室);The University of Tennessee(田纳西大学)