A Near-Optimal Algorithm for Safe Reinforcement Learning Under Instantaneous Hard Constraints

In many applications of Reinforcement Learning (RL), it is critically important that the algorithm performs safely, such that instantaneous hard constraints are satisfied at each step, and unsafe states and actions are avoided. However, existing algorithms for "safe" RL are often designed under constraints that either require expected cumulative costs to be bounded or assume all states are safe. Thus, such algorithms could violate instantaneous hard constraints and traverse unsafe states (and actions) in practice. Therefore, in this paper, we develop the first near-optimal safe RL algorithm for episodic Markov Decision Processes with unsafe states and actions under instantaneous hard constraints and the linear mixture model. It not only achieves a regret Õ( dH 3 √ dK ∆c ) that tightly matches the state-of-the-art regret in the setting with only unsafe actions and nearly matches that in the unconstrained setting, but is also safe at each step, where d is the feature-mapping dimension, K is the number of episodes, H is the number of steps in each episode, and ∆ c is a safety-related parameter. We also provide a lower bound Ω(maxdH , which indicates that the dependency on ∆ c is necessary. Further, both our algorithm design and regret analysis involve several novel ideas, which may be of independent interest. Recently, instantaneous hard constraints have been studied in theoretical machine learning. Specifically, [12] and [18] studied bandits with linear instantaneous constraints that require a linear safety value of the chosen action to be bounded at each step. However, it is well-known that bandits are only a very special case of MDP. [14] studied safe linear MDP with linear instantaneous hard constraints. However, they still assume that only the actions could be unsafe, and hence unsafe states (and transitions) are still not considered. Intuitively, when there are only unsafe actions, any action will