arXiv subjects

Sunyoung An

Publications and source records attributed to Sunyoung An.

3 recordsLinked to original sources

arXiv2026

Adaptive Optimizers Can Get a Policy Ranking Wrong: Momentum, Dependent Data, and a Two-Run Remedy

Operators choosing among decision rules, such as when a battery charges or where an idle taxi goes, rank them by estimated long-run value. A standard estimator, linear temporal-difference (TD) learning, fits values from one stream of correlated observations. Large fits often use an adaptive optimizer, such as adaptive moment estimation (Adam), with fixed averaging rates. We show that these rates can change what is estimated, not just how fast: the same observations drive the updates and the optimizer's step-size scaling, moving the fit away from the intended TD value. The shift differs across rules, so it need not cancel in a comparison, and more data only makes a wrong ranking look more certain. Our remedy refits the same data at a second averaging rate that halves the effective gain, the number to which the leading shift is proportional. Twice the new fit minus the original removes that shift. In New York taxi and battery models calibrated to real data, common optimizer settings leave the selected rule unchanged but order close rules wrongly and misstate its value. Our remedy corrects nearly every wrong ordering, with one extra fit when the shift is moderate and two when it is larger.

stat.ML↗

arXiv2026

A Polyak-Ruppert Central Limit Theorem for SA-Adam with Momentum and Non-Convergent Adaptive Preconditioning

Adaptive optimizers combining preconditioning, momentum, and weight decay (Adam and AdamW) are, under Polyak-Ruppert averaging, candidate engines for one-pass inference. Does the averaged iterate keep the classical Polyak-Ruppert central limit theorem (CLT), with sandwich covariance $H^{-1}SH^{-1}$ (Hessian $H$, gradient covariance $S$), under momentum and non-convergent preconditioning? The preconditioner-only analysis does not carry over: with momentum the canonical decomposition collapses to a tautology. Treating the augmented state (iterate, momentum buffer) as a time-varying linear stochastic approximation (SA), we prove (under local stabilization) positive drift stability, a non-autonomous Polyak-Ruppert CLT, and a projection identity. The upshot: the iterate-marginal covariance is exactly the plain stochastic gradient descent (SGD) sandwich $H^{-1}SH^{-1}$, so the adaptivity is asymptotically invisible. This holds for SA-Adam (sub-linearly vanishing momentum gain, $γ\in(α,1)$; the sub-linear regime is essential), not constant-$β$ deployed Adam. Coupled $L_2$ weight decay yields the ridge-penalized sandwich, extending one-pass inference to regularized problems.

math.ST↗

arXiv2026

When Does Dynamic Preconditioning Preserve the Polyak-Ruppert CLT? A Stabilization Threshold

Polyak-Ruppert averaging yields an asymptotically normal estimator with sandwich covariance $H^{-1}SH^{-1}$, the foundation of online inference. When the gradient step is preconditioned by a data-driven matrix $P_t$, we ask how fast $P_t$ must stabilize for the central limit theorem (CLT) to remain valid. We resolve this via an exact preconditioner-isolating decomposition of the averaged error that confines $P_t$ to a dynamic remainder $R_n$, leaving the martingale and Taylor terms preconditioner-free. Let $M_t = (P_t H)^{-1}$ denote the effective inverse drift matrix, with $\|M_t - M_{t-1}\|_{\mathrm{op}} \lesssim t^{-β}$ and step-size exponent $α\in (1/2, 1)$. We identify a stabilization-rate threshold $β> (α+1)/2$ and prove that, within the class of polynomial rate hypotheses used in our upper bound, it cannot be weakened: the dynamic remainder $\sqrt{n}\,R_n$ vanishes in $L^2$ whenever $β> (α+1)/2$, and we exhibit sequences satisfying those hypotheses for which it does not vanish when $β\le (α+1)/2$. A single stabilization argument certifies three SA variants - SA-AdaGrad, SA-RMSProp, and SA-ONS - with gain $ρ_t = c/t$, each delivering one-step $L^2(\mathrm{op})$ stabilization of order $t^{-1}$, yielding the CLT $\sqrt{n}(\bar{x}_n - x^*) \to N(0, H^{-1}SH^{-1})$; under bounded inputs the pathwise rate $β= 1$ further preserves the $n^{-1/6}$ Wasserstein rate at $α^* = 2/3$. Under standard regularity conditions, Wald-type online inference remains valid for dynamically preconditioned averaged SGD whose stabilization rate exceeds the threshold.

math.ST↗