  Robust Reinforcement Learning (RRL) is a promising Reinforcement Learning
(RL) paradigm aimed at training robust to uncertainty or disturbances models,
making them more efficient for real-world applications. Following this
paradigm, uncertainty or disturbances are interpreted as actions of a second
adversarial agent, and thus, the problem is reduced to seeking the agents'
policies robust to any opponent's actions. This paper is the first to propose
considering the RRL problems within the positional differential game theory,
which helps us to obtain theoretically justified intuition to develop a
centralized Q-learning approach. Namely, we prove that under Isaacs's condition
(sufficiently general for real-world dynamical systems), the same Q-function
can be utilized as an approximate solution of both minimax and maximin Bellman
equations. Based on these results, we present the Isaacs Deep Q-Network
algorithms and demonstrate their superiority compared to other baseline RRL and
Multi-Agent RL algorithms in various environments.
