Gradient Descent Exponent

Upper bound, last-listed row

| 2 | Folklore | See, e.g., [N2014] |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $\log_2(1+\sqrt{2}) \approx 1.271$ | [AP24] | Obtained by the "silver stepsize schedule". Conjecturally optimal. Appeared on arXiv concurrently with [GSW23]. |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row 1 line 19 whose comment cites [B2015] — the claim we checked: that Bertsekas's Convex Optimization Algorithms (2015), cited as an example in the row's comment, states that constant step sizes achieve the listed exponent 1. What we read could not settle it: the book's overview of descent methods (Section 2.1.1, pp. 60–61) states an O(1/k) bound on the function gap for "a properly chosen constant stepsize, and under some reasonable conditions (Lipschitz continuity of ∇f)"; whether those conditions cover this constant's class of functions was not checked. This verdict does not cover the row's credit to folklore. source link (read in Chapter 2 of the book as the author posts it, and in the book's contents; Section 6.1, to which that passage refers, could not be reached on the author's site, Athena Scientific's site, Google Books or the Internet Archive). Selected: drawn by its position in the list of cited rows, not because it looked wrong.

1 bound row(s) here have been checked against material for their cited source (1 drawn by position, 0 chosen because something already looked wrong). Across this whole ledger 70 row(s) have been drawn by position, against 691 rows that name a source, counted on 2026-09-27: 64 were checked against material for their cited sources and for 6 the cited source could not be read at all. 5 more were chosen for suspicion and checked; they are counted apart, because a set selected for suspicion carries no rate. A row not listed here has NOT been checked.