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Efficient Optimistic Exploration in Linear-Quadratic Regulators via Lagrangian Relaxation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Lagrangian relaxation with an extended control and dichotomy search | OFULQplus for LQR · LQR, T steps | regret: OFULQplus has a \sqrt{\kappa} dependence in its leading displayed term; LAGLQ has a \kappa^{3/2} dependence | Helped |
| Relax the per-step confidence constraint to an asymptotic average constraint (ablation) | OFULQplus · LQR, T steps | regret: OFULQplus: \wt O\Big( \!\big( \kappa \|P_*\|_2^{2}\!+\!\sqrt{\kappa} \|P_*\|^{3/2}_2 (n\! +\! d) \!\sqrt{n}\big) \sqrt{T | Hurt |
| Use isotropic perturbations instead of confidence-based optimism | LQR exploration · LQR, T steps | regret: \mathcal{R}_{\cecce} = \wt O\big( \|P^*\|_2^{11/2} d\sqrt{n T}\big); \mathcal{R}_{\laglq} = \wt{O} \big( \kappa^{3/2} \| | Hurt |
| Use DSLLQ to solve the relaxed extended LQR | LAGLQ · LQR, accuracy ε | Riccati and Lyapunov equation solves: O\big(\log(\mu_{\max} /\epsilon) \big) | Helped |
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