Gradient-based learning in multi-agent systems is difficult because the gradient derives from a first-order model which does not account for the interaction between agents' learning processes. LOLA (arXiv:1709.04326) accounts for this by differentiating through one step of optimization. We propose to judge joint policies by their long-term prospects as measured by the meta-value, a discounted sum over the returns of future optimization iterates. We apply a form of Q-learning to the meta-game of optimization, in a way that avoids the need to explicitly represent the continuous action space of policy updates. The resulting method, MeVa, is consistent and far-sighted, and does not require REINFORCE estimators. We analyze the behavior of our method on a toy game and compare to prior work on repeated matrix games.

翻译：多智能体系统中的梯度学习存在困难，因为梯度源自一阶模型，该模型未考虑智能体学习过程之间的相互作用。LOLA（arXiv:1709.04326）通过一次优化步骤的微分来应对这一问题。我们提出根据联合策略的长期前景（以元价值衡量）来评判它们，元价值是未来优化迭代回报的折现总和。我们将一种形式的Q学习应用于优化的元博弈，从而避免显式表示策略更新的连续动作空间。由此产生的方法MeVA具有一致性和远见性，且无需REINFORCE估计器。我们在一个玩具游戏上分析了该方法的行为，并与重复矩阵博弈中的先前工作进行了比较。