Research map / Learning theory and algorithms / Sample complexity
Certainty Equivalence is Efficient for Linear Quadratic Control
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the certainty equivalent controller instead of robust synthesis | LQR with sufficiently small model error · LQR | suboptimality gap: \mathcal{O}(\varepsilon) -> \mathcal{O}(\varepsilon^2) | Helped |
| Use certainty equivalent control with ε-greedy exploration and variance schedule σ²η,t ∼ t⁻¹ᐟ² | Online LQR · Adaptive LQR | regret: \widetilde{\mathcal{O}}(T^{2/3}) -> \widetilde{\mathcal{O}}(\sqrt{T}) | Helped |
| Apply the certainty equivalent controller to partially observed systems with estimates aligned up to a unitary transform | LQG · LQG | suboptimality gap: \mathcal{O}(\varepsilon^2) | Helped |
| Use certainty equivalent control in place of a robust controller | LQR at moderate estimation error · LQR | suboptimality gap: \mathcal{O}(\varepsilon^2) versus \mathcal{O}(\varepsilon) | Mixed |
| Use the direct controllability-based Riccati perturbation bound rather than the operator-theoretic bound | Example with A⋆ = 1.01 · I₂ and B⋆ = diag(1, β) · Riccati perturbation example | Riccati solution error bound: \mathcal{O}(\varepsilon / \beta^4) -> \mathcal{O}(\varepsilon / \beta^3) | Helped |
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