# Level-Based Analysis of the Population-Based Incremental Learning Algorithm

arXiv: https://arxiv.org/abs/1806.01710 · HTML: https://mlsanity.com/paper/1806.01710/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2018.

## Built on by (most cited first, 1 of 1)

- [Choosing the Right Algorithm With Hints From Complexity Theory](https://mlsanity.com/paper/2109.06584/) (2021)

## Abstract (arXiv)

The Population-Based Incremental Learning (PBIL) algorithm uses a convex combination of the current model and the empirical model to construct the next model, which is then sampled to generate offspring. The Univariate Marginal Distribution Algorithm (UMDA) is a special case of the PBIL, where the current model is ignored. Dang and Lehre (GECCO 2015) showed that UMDA can optimise LeadingOnes efficiently. The question still remained open if the PBIL performs equally well. Here, by applying the level-based theorem in addition to Dvoretzky--Kiefer--Wolfowitz inequality, we show that the PBIL optimises function LeadingOnes in expected time O(nλ log λ + n2) for a population size λ = Omega(log n), which matches the bound of the UMDA. Finally, we show that the result carries over to BinVal, giving the fist runtime result for the PBIL on the BinVal problem.