  Reinforcement learning (RL) agents are vulnerable to adversarial
disturbances, which can deteriorate task performance or compromise safety
specifications. Existing methods either address safety requirements under the
assumption of no adversary (e.g., safe RL) or only focus on robustness against
performance adversaries (e.g., robust RL). Learning one policy that is both
safe and robust remains a challenging open problem. The difficulty is how to
tackle two intertwined aspects in the worst cases: feasibility and optimality.
Optimality is only valid inside a feasible region, while identification of
maximal feasible region must rely on learning the optimal policy. To address
this issue, we propose a systematic framework to unify safe RL and robust RL,
including problem formulation, iteration scheme, convergence analysis and
practical algorithm design. This unification is built upon constrained
two-player zero-sum Markov games. A dual policy iteration scheme is proposed,
which simultaneously optimizes a task policy and a safety policy. The
convergence of this iteration scheme is proved. Furthermore, we design a deep
RL algorithm for practical implementation, called dually robust actor-critic
(DRAC). The evaluations with safety-critical benchmarks demonstrate that DRAC
achieves high performance and persistent safety under all scenarios (no
adversary, safety adversary, performance adversary), outperforming all
baselines significantly.
