Safe Reinforcement Learning with Linear Function Approximation
This addresses safety-critical systems where avoiding catastrophic failures is essential, though it is incremental as it builds on existing linear function approximation methods.
The paper tackles the problem of ensuring safety in reinforcement learning by modeling safety as an unknown linear cost function and proposes algorithms (SLUCB-QVI and RSLUCB-QVI) that strictly avoid unsafe actions while achieving a regret bound of $ ilde{\mathcal{O}}\left(κ\sqrt{d^3H^3T} ight)$, nearly matching unsafe algorithms.
Safety in reinforcement learning has become increasingly important in recent years. Yet, existing solutions either fail to strictly avoid choosing unsafe actions, which may lead to catastrophic results in safety-critical systems, or fail to provide regret guarantees for settings where safety constraints need to be learned. In this paper, we address both problems by first modeling safety as an unknown linear cost function of states and actions, which must always fall below a certain threshold. We then present algorithms, termed SLUCB-QVI and RSLUCB-QVI, for episodic Markov decision processes (MDPs) with linear function approximation. We show that SLUCB-QVI and RSLUCB-QVI, while with \emph{no safety violation}, achieve a $\tilde{\mathcal{O}}\left(κ\sqrt{d^3H^3T}\right)$ regret, nearly matching that of state-of-the-art unsafe algorithms, where $H$ is the duration of each episode, $d$ is the dimension of the feature mapping, $κ$ is a constant characterizing the safety constraints, and $T$ is the total number of action plays. We further present numerical simulations that corroborate our theoretical findings.