布洛托上校博弈模型及求解方法研究进展

doi:10.11896/jsjkx.230600011

摘要/Abstract

摘要： 对抗条件下的资源分配是大多数博弈决策问题的核心。从拟合最优解到博弈均衡解,基于博弈论的资源分配策略求解是认知决策领域的前沿课题。文中围绕对抗条件下资源分配的布洛托上校博弈模型和求解方法展开综述分析。首先,简要介绍了离线与在线策略学习的区别,策略博弈与相关解概念,在线优化与遗憾值;其次,梳理了6类布洛托上校博弈典型模型(连续布洛托上校博弈、离散布洛托上校博弈、广义布洛托上校博弈、广义乐透布洛托博弈、广义规则布洛托上校博弈与在线离散布洛托上校博弈);然后,区分2个阶段(离线与在线)3类博弈场景(单次、重复、多阶段),分析了多类布洛托上校博弈求解方法;最后,从典型应用探索、广义博弈模型、博弈求解方法、未来研究展望共4方面进行了未来研究前沿分析及展望。通过对当前布洛托上校博弈进行概述,期望能为对抗条件下资源分配与博弈论相关领域的研究带来启发。

关键词: 资源分配, 布洛托上校博弈, 近似纳什均衡, 在线凸优化, 期望遗憾, 高概率遗憾

Abstract: Resource allocation under confrontation conditions is the core of most game decision problems.From fitting optimal solution to game equilibrium solution,resource allocation strategy solving based on game theory is a frontier topic in cognitive decision-making field.This paper summarizes and analyzes the Colonel Blotto game model and its solution method for adversarial resource allocation.Firstly,the differences between offline and online strategy learning,strategy game and related solution concepts,online optimization and regret value are briefly introduced.Secondly,six types of Colonel Blotto game models(continuous Blotto game,discrete Colonel Lotto game,generalized Colonel Blotto game,generalized Lotto Blotto game,generalized rule Colonel Lotto game and online discrete Colonel Lotto game).Then,this paper distinguishes 2 stages(offline and online) and 3 types of game scenarios(single,repeated,multi-stage),and analyzes the solution method of Colonel Blotto game.Finally,the future research frontiers are analyzed and prospected from four aspects:typical application exploration,generalized game model,game solving method and future research prospect.The main purpose is to give an overview of the current Colonel Blotto game,hoping to enlighten the research on resource allocation and game theory under confrontation condition.

Key words: Resource allocation, Colonel Blotto game, Approximate Nash equilibrium, Online convex optimization, Expected regret, High-probability regret

中图分类号:

TP181

罗俊仁, 邹明我, 陈少飞, 张万鹏, 陈璟. 布洛托上校博弈模型及求解方法研究进展[J]. 计算机科学, 2024, 51(1): 84-98. https://doi.org/10.11896/jsjkx.230600011

LUO Junren, ZOU Mingwo, CHEN Shaofei, ZHANG Wanpeng, CHEN Jing. Research Progress on Colonel Blotto Game Models and Solving Methods[J]. Computer Science, 2024, 51(1): 84-98. https://doi.org/10.11896/jsjkx.230600011

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