Optimal Stochastic Bilevel Optimization with First-Order Oracles EDG9ZFDSWK

URI	`m2://res/EDG9ZFDSWK`
Kind	preprint
Creators	Linxuan Pan, Junchi Yang
Date	2026-10-01
MSC	49-XX, 90-XX, 93-XX
Subjects	arxiv math.OC, arxiv cs.LG
Scope	in

Expressions

e1: version, preprint

Language	en
Date	2026-10-01
Ids	arXiv 2610.01843

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Properties of the scaled pair	statement	proposition B.6	arxiv
Outer-direction error and objective descent	statement	lemma A.6	arxiv
Errors caused by the current lower iterate	statement	lemma A.2	arxiv
Admissible primitive oracle	statement	lemma B.21	arxiv
Projection accumulation; cf. Lemma 12	statement	lemma B.8	arxiv
Hard objective and comparison oracle	statement	proposition 4.1	arxiv
Compressed hard-chain properties	statement	lemma B.4	arxiv
Lower response	statement	lemma B.18	arxiv
Hard-chain properties	statement	lemma B.1	arxiv
Normalized finite-difference error	statement	lemma A.3	arxiv
Sequential posterior-stabilizer invariance	statement	lemma B.10	arxiv
Uniform frontier split	statement	lemma B.2	arxiv
Conditional decomposition of the three updates	statement	lemma A.4	arxiv
Bilevel gradient and primitive variance	statement	proposition 4.2	arxiv
Tracking after the outer point moves	statement	lemma A.7	arxiv
Regularity of the lower solution and auxiliary target	statement	lemma A.1	arxiv
Soft projection and known postprocessing	statement	corollary B.15	arxiv
Invariant posterior under an invariant observation	statement	lemma B.9	arxiv
Compressed correction bounds	statement	lemma B.5	arxiv
Lower bound for bilevel problems	statement	theorem 4.3	arxiv
JAM1WAPACN	statement	theorem 3.1	arxiv
Conditional residual spherical law; cf. Lemma 14	statement	lemma B.11	arxiv
Two-vector probability-$\varpi$ zero-chain	statement	corollary B.3	arxiv
One-pair guessing estimate; cf. Lemma 13	statement	lemma B.12	arxiv
Projected auxiliary correction at the current outer point	statement	lemma A.5	arxiv
Uniform order-$p$ regularity	statement	lemma B.20	arxiv
Uniform finite-channel probability-$\varpi$ zero-chain	definition	definition B.7	arxiv
Primitive simulation and conditional variance	statement	lemma B.17	arxiv
Controlled perturbation of the hard objective	statement	corollary B.19	arxiv
Terminal output	statement	corollary B.14	arxiv
Variance and the ordinary first-order lower bound	statement	lemma B.16	arxiv
Finite-channel random rotation	statement	lemma B.13	arxiv
A uniform one-step inequality	statement	proposition A.8	arxiv

Catalogue records

arxiv: 2610.01843 (work)
arxiv_text: 2610.01843 (work)