Safely Learning Dynamical Systems from Short Trajectories

The paper’s Theorem 1 states that the feasible set of the robust problem (7) is exactly the projection (onto x) of the LP (8), and it proves this by dualizing the inner LP over A (equations (9)–(10)), invoking strong duality, and using weak/strong duality to show equivalence of feasible sets and equality of optimal values. The candidate solution reproduces the same construction: it expresses h_i^T A x as a Frobenius inner product, forms the Lagrangian, derives the same dual feasibility identity x h_i^T = Σ_k x_k η_k^{(i)T} + Σ_j μ_j^{(i)} V_j^T, and uses weak/strong duality to prove projection equivalence and value equality. This matches the paper’s argument essentially step-by-step, with slightly more derivational detail and an explicit note that U_m is nonempty (which holds in the paper’s setting since A? ∈ U_k by construction). Hence both are correct and substantially the same proof. See Theorem 1 and its proof (stating (7)–(8) and the dualization via (9)–(10)) in the paper ; the problem setup (U0, S, Uk, and (7)) appears in Section 3.1 .