Safe Reinforcement Learning with Linear Function Approximation

Abstract

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 $\tilde{\mathcal{O}}\left(\kappa \sqrt{d^3{H}^{3}T}\right)$ 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, $\kappa$ 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.

References in corpus (14)

• Safe Model-based Reinforcement Learning with Stability Guarantees
• Reward Constrained Policy Optimization
• Provably Efficient Reinforcement Learning with Linear Function Approximation
• Safe Exploration in Finite Markov Decision Processes with Gaussian Processes
• Safe Reinforcement Learning in Constrained Markov Decision Processes
• Safe Reinforcement Learning via Curriculum Induction
• Provably Efficient Safe Exploration via Primal-Dual Policy Optimization
• Exploration-Exploitation in Constrained MDPs
• Convergent Policy Optimization for Safe Reinforcement Learning
• Constrained Upper Confidence Reinforcement Learning
• Provably Efficient Q-Learning with Low Switching Cost
• Upper Confidence Primal-Dual Reinforcement Learning for CMDP with Adversarial Loss
• Stochastic Bandits with Linear Constraints
• Decentralized Multi-Agent Linear Bandits with Safety Constraints