Geometry-Aware Multi-Objective Optimization: Norm-Constrained Oracles with Entropic Weight Updates E75XQY0QFM

URI	`m2://res/E75XQY0QFM`
Kind	preprint
Creators	El Mahdi Chayti, Alireza Mirrokni, Martin Jaggi
Date	2026-10-09
MSC	49-XX, 90-XX, 93-XX
Subjects	arxiv math.OC, arxiv cs.LG
Scope	in

Expressions

e1: version, preprint

Language	en
Date	2026-10-09
Ids	arXiv 2610.13773

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
2GPF9YV710	statement	lemma F.2	arxiv
Stochastic one-step inequality	statement	lemma D.2	arxiv
Uniqueness of the optimal blended gradient	statement	proposition 3.1	arxiv
Bias of the regularized target	statement	lemma F.7	arxiv
Tracking error	statement	lemma 4.8	arxiv
Weight increment under noisy scores	statement	lemma 4.7	arxiv
Deterministic rate	statement	theorem 4.4	arxiv
Tracking recursion	statement	lemma F.6	arxiv
Stationary points of fixed scalarizations are Pareto stationary	statement	proposition 3.2	arxiv
Sensitivity of the regularized optimum	statement	lemma F.4	arxiv
Trajectory gradient bound	statement	lemma 4.3	arxiv
Inner regret on bounded gradient sequences	statement	theorem 4.5	arxiv
Descent lemma in a norm pair	statement	lemma A.1	arxiv
Subgradient of the weight objective	statement	lemma A.3	arxiv
MGE2YBPV2N	statement	proposition G.1	arxiv
Gradient bound from the function value	statement	lemma A.2	arxiv
KL perturbation of the first argument	statement	lemma F.5	arxiv
Regularized entropic mirror descent	statement	lemma 4.2	arxiv
Iteration-wise inner gap, with progress	statement	theorem 5.1	arxiv
Stochastic rate	statement	theorem 4.9	arxiv
Iteration-wise CA distance under uniform convexity	statement	corollary 5.2	arxiv
QXMX1X1CSE	statement	lemma D.1	arxiv
When the oracle output is conflict-avoidant	statement	proposition B.1	arxiv
Polylogarithmic $K$ under sub-Gaussian noise	statement	corollary D.4	arxiv
Stochastic inner regret	statement	corollary D.3	arxiv
Static regret to gap decomposition	statement	corollary 4.6	arxiv
Contraction toward the regularized target	statement	lemma F.3	arxiv
Average CA distance	statement	corollary C.1	arxiv
Closed form of line 6	statement	lemma F.1	arxiv
One-step inequality	statement	lemma 4.1	arxiv
Stationarity, CA distance, inner gap	definition	definition 3.1	arxiv
ZT5AHE72R1	statement	proposition H.1	arxiv

Catalogue records

arxiv: 2610.13773 (work)
arxiv_text: 2610.13773 (work)