MathDBLast-iterate convergence conjecture in definable optimization
Last-iterate convergence conjecture in definable optimization
Let be the iterates generated by the mini-batch stochastic approximation framework under the hypotheses stated in Remark 12 of Bolte and Pauwels (2021), with definable potentials. The conjecture asserts that converges almost surely.
Sources & referencesView supporting material
Primary source
Additional references
- A Mini-Batch Counterexample to Last-Iterate Convergence in Definable Optimization — arXiv — Weiwei Kong
Progress summary
A new preprint claims that the advertised convergence guarantee fails for mini-batch stochastic optimization, so the problem is not settled.
The conjecture concerns whether last iterates in definable mini-batch stochastic approximation must converge under the stated assumptions. The reported construction directly challenges the claim made in Remark 12 of Bolte and Pauwels (2021).
August 2026 counterexample claim
Weiwei Kong's preprint, “A Mini-Batch Counterexample to Last-Iterate Convergence in Definable Optimization,” claims an explicit counterexample and therefore refutes the stated convergence claim. The result has not been independently verified in the retrieved material.
Current status (as of August 2026): A preprint claims the conjecture is false under the stated assumptions, but independent verification is absent; convergence under stronger step-size conditions remains unaffected.
Mini-batch last-iterate convergence conjecture refuted
Mini-batch last-iterate convergence conjecture refuted
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