学习参数化单调博弈
Learning Parametric Monotone Games
浏览论文内容
中文总结 AI 辅助
针对所有参数值下单调的参数化纳什均衡问题，提出两种学习方法，可在两种场景下高效求解，经数值示例验证适用，相关Python库及示例公开可用。
中文摘要 AI 辅助
我们研究从数据中学习在所有参数值下均为单调（或强单调）的参数化纳什均衡（NE）问题。在存在局部且共享的凸约束时，单调性可实现高效计算所学博弈的广义纳什均衡。我们考虑两种学习场景：（i）从智能体的代价样本中直接学习NE问题；（ii）从智能体的最优响应样本中逆学习替代智能体的代价。我们提出两种方法解决这些任务：第一种是基于惩罚的方法，在训练过程中促进所学博弈的单调性；第二种基于我们为一类广泛单调博弈引入的表示定理，对智能体的代价进行参数化，使得无论使用何种训练数据，NE问题的单调性在所有参数值下均由构造保证。我们在多个数值示例中说明了所提方法的适用性，论文中报告的Python库及示例可在该https URL获取。
英文摘要
We study the problem of learning from data a parametric Nash equilibrium (NE) problem that is monotone (or strongly monotone) for all parameter values. In the presence of local and shared convex constraints, monotonicity enables efficient computation of generalized Nash equilibria of the learned game. We consider two learning scenarios: (i) direct learning of the NE problem from samples of the agents' costs, and (ii) inverse learning of surrogate agents' costs from samples of their best responses. We propose two methods to solve these tasks. The first is a penalty-based approach that promotes monotonicity of the learned game during training. The second, based on a representation theorem we introduce for a broad class of monotone games, parameterizes the agents' costs so that monotonicity of the NE problem is guaranteed by construction, for all parameter values, regardless of the training data used. We illustrate the applicability of the proposed methods on several numerical examples. A Python library and the examples reported in the paper are available at https://github.com/bemporad/learn_monotone_games.
发表机构
- IMT School for Advanced Studies（IMT高等研究院）
- TU Darmstadt（达姆施塔特工业大学）
机构由 AI 辅助整理，请以论文原文为准。
