As a summary, this paper makes the following contributions.

However, all the above results are limited to the deterministic setting.

The design automation of analog circuits poses significant challenges in terms of the large design space, complex interdependencies between circuit specifications, and resource-intensive simulations.

In Equation 4, maximization is carried out over the inputy to the inverse-map, and the input z which is captured inˆp in the above optimization problem, i.e. maximization overz in Equation 4 is equivalent to choosingˆp subject to the choice of singleton/ Dirac-deltaˆp. Since Equation 4 describes a constrained optimization problem, our approach towards solving this problem in practice is via dual gradient descent. Gradient descent is used to optimize the Lagrangian of Equation 4 (with the constraintp(z) 2 modified to belogp(z) 2 as it is easy to uselogp(z)numerically for stochasticoptimization),showninEquation5. Ateachiteration,itsamplesafunction from this distribution and queries the pointx?t that greedily minimizes this function. Information Ratio Russo and Van Roy[30] related the expected regret of TS to its expected information gain i.e. the expected reduction in the entropy of the posterior distribution ofX .

MINs can scale to high-dimensional input spaces and leverage offline logged data for both contextual and non-contextual optimization problems.

Zhang et al. have recently shown that geodesic convex concave Riemannian problems always admit saddle-point solutions.