Our numerical experiments verify these guarantees.

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic convergence, have slow sublinear rates, or require strong assumptions. To address these challenges, we propose a penalization framework that delineates the relationship between approximate solutions of the original problem and its reformulated counterparts.

In modern chip design, placement aims at placing millions of circuit modules, which is an essential step that significantly influences power, performance, and area (PP A) metrics.

Optimizing discrete black box functions is key in several domains, e.g. protein engineering and drug design. Due to the lack of gradient information and the need for sample efficiency, Bayesian optimization is an ideal candidate for these tasks. Several methods for high-dimensional continuous and categorical Bayesian optimization have been proposed recently. However, our survey of the field reveals highly heterogeneous experimental set-ups across methods and technical barriers for the replicability and application of published algorithms to real-world tasks. To address these issues, we develop a unified framework to test a vast array of high-dimensional Bayesian optimization methods and a collection of standardized black box functions representing real-world application domains in chemistry and biology.

Secondly, these works do not account for finite-sampling errors in the obtained curve.

V on Neumann's celebrated minimax theorem establishes the existence of Nash equilibrium in all two-player zero-sum games where the players' utilities are continuous as well as concave in their