Fundamental sample-efficiency gap for robust control

Prove or refute the conjecture that robust control incurs a fundamental asymptotic sample-efficiency gap relative to certainty equivalence and domain randomization in learning the linear quadratic regulator, by developing lower bounds that preclude the 1/N trace rate achieved by CE and DR.

Background

The paper’s upper bounds show that RC’s leading term depends on dθ and the operator norm of H(θ⋆)FI(θ⋆)^{-1}, while CE and DR match the optimal 1/N trace rate. The authors conjecture the RC gap is fundamental, reflecting its conservative worst-case design.

A definitive lower bound would formalize RC’s intrinsic inefficiency relative to CE and DR and guide the choice of synthesis methods in low- versus high-data regimes.