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Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use robust SLS-based adaptive control with explicit exploration and FIR synthesis | Adaptive LQR · Adaptive LQR | regret: \widetilde{\mathcal{O}}(T^{2/3}) upper bound; \widetilde{\Omega}(T^{2/3}) expected lower bound | Mixed |
| Use the robust adaptive method instead of heuristic OFU or Thompson Sampling | Adaptive LQR methods · Marginally unstable Laplacian example | regret | No clear effect |
| Use robust adaptive control instead of OFU or Thompson Sampling | Adaptive LQR methods · Marginally unstable Laplacian example | infinite-horizon LQR cost | Helped |
| Add a constraint on the system response | Robust adaptive synthesis · Demand forecasting with state constraints | state magnitude | Helped |
| Inject exploration noise using variance schedule σ_{η,i}² = σ_w² (T_i/C_T)^{-1/3} | Robust Adaptive Control Algorithm · Adaptive LQR | regret: \widetilde{\mathcal{O}}(T^{2/3}) | Mixed |
| Use an algorithm with regret O(T^α) to obtain parameter estimation rate O(T^{-α/2}) | Adaptive control algorithms · Adaptive LQR | parameter estimation rate: \mathcal{O}(T^{\alpha}); \mathcal{O}(T^{-\alpha/2}) | Mixed |
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