אופטימיזציה בילוולית סטוכסטית: קצבי התקדמות משופרים ללא תנאי הבקרה הנדיר

תקציר מקורי באנגליתarXiv:2609.06580v1 Announce Type: cross Abstract: We investigate stochastic simple bilevel optimization with smooth and possibly nonconvex upper- and lower-level objectives. Existing stochastic extensions of dynamic barrier gradient descent (DBGD) either obtain fast convergence under an unverifiable trajectory-dependent ``rare-visit'' assumption, or remove this assumption at a substantially higher oracle cost. We show that a simple denominator-only regularization of the DBGD multiplier eliminates the need for such an assumption while preserving fast convergence rates. Specifically, our method achieves $(\varepsilon, \varepsilon)$-stationarity in $O(\varepsilon^{-2})$ iterations using $O(\varepsilon^{-4})$ upper-level and $O(\varepsilon^{-7})$ lower-level stochastic gradients, which improve