Executive summary
Paper setting
The paper studies convex minimization on a compact convex domain with a Bregman regularizer. Its Lévy mirror flow is
[ dY(t)=-\nabla f(X(t)),dt+dL(t),\qquad X(t)=\operatorname{mirror}(\eta(t)Y(t)), ]
where the centered Lévy process has finite p-th moments for p in (1,2] and
can have jumps with infinite variance when p<2. The discrete stochastic dual
averaging update is Y[t+1]=Y[t]-(∇f(X[t])+noise[t]) followed by
X[t+1]=mirror(η[t+1]Y[t+1]).
The reproduction uses the paper’s bounded Euclidean instance
X=[-1,1], h(x)=x²/2, and mirror(z)=clip(ηz,-1,1). Symmetric Pareto
compound-Poisson jumps have tail index alpha=p+0.12, so their p-th moment is
finite while the p<2 cases remain heavy-tailed. Brownian increments provide the
tame component where stated. Huber objectives are convex and 1/δ-smooth on
each tested branch; quadratic objectives are used for strong-convexity controls.
Independent evidence
| claim | seeds/trials | sweep | decisive result |
|---|---|---|---|
| 1 | 8 seeds | p={1.25,1.5,1.75,2}, T={256,…,4096} |
4/4 measured gaps below the paper’s explicit R0(T) bound; gap varies across both sweeps |
| 2 | 8 seeds per cell | 5 eta values, three heavy p values plus tame p=1.5 | every measured stationary MSE is below the paper radius; heavy and tame treatments have distinct eta slopes |
| 3 | 8 seeds per cell | p={1.5,1.75}, five δ values |
40/40 first-passage cells uncensored and below the explicit Theorem-3 bound |
| 4 | 8 seeds | p={1.25,1.5,1.75,2}, T={512,…,8192} |
SDA and LMF gaps vary with T and pass their respective paper rate bounds in every displayed cell |
| 5 | 20 seeds per cell | p={1.5,1.75}, four ε values |
measured iteration counts increase as ε tightens; reverse-drift control reaches 0/20 seeds |
| 6 | 12 paths per branch | Huber thresholds a={1,1.5,2} |
correction-on inequality passes 12/12 in every branch; correction-off control passes 0/12 |
The code computes means and standard errors across independent seeds. No paper figure, printed result, or peer logbook is parsed as a result source.