Safety
Near-Optimal Regret for the Safe Learning-based Control of the Constrained Linear Quadratic Regulator
arXiv:2604.22158v1 Announce Type: cross Abstract: We study the problem of adaptive control of the stochastic linear quadratic regulator (LQR) with constraints that must be satisfied at every time step
arXiv:2604.22158v1 Announce Type: cross Abstract: We study the problem of adaptive control of the stochastic linear quadratic regulator (LQR) with constraints that must be satisfied at every time step. Prior work on the multidimensional problem has shown ilde{O}(T^{2/3}) regret and satisfaction of robust constraints, leaving open the question of whether ilde{O}(sqrt{T}) regret can be attained in the constrained LQR setting. We contribute to this problem by showing ilde{O}(sqrt{T}) regret and satisfaction of chance constraints. This type of constraints allow us to handle unbounded noise and also enable analytical techniques not directly applicable to robust constraints. Our proposed algorithm for this problem uses an SDP to select an optimistic policy, and then "scales back" this policy until it is verifiably-safe. Our theoretical analysis establishes regret and constraint guarantees via a key lemma that bounds the system covariance in terms of the chosen policy. This covariance-based analysis is in contrast with the cost-to-go based analysis that is typically used in adaptive LQR.
Related
- Near-Optimal Policy Identification in Robust Constrained Markov Decision Processes via Epigraph Form
- A Two-Timescale Primal-Dual Framework for Reinforcement Learning via Online Dual Variable Guidance
- Lever: Inference-Time Policy Reuse under Support Constraints
- Restless Bandits with Individual Penalty Constraints: A New Near-Optimal Index Policy and How to Learn It
- Offline-Online Reinforcement Learning for Linear Mixture MDPs
Source: arXiv cs.LG | 2026-04-27