# Power of human-algorithm collaboration in solving combinatorial optimization problems

arXiv: https://arxiv.org/abs/2107.11784 · HTML: https://mlsanity.com/paper/2107.11784/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 25 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Human-in-the-loop Artificial Intelligence](https://mlsanity.com/paper/1710.08191/) (2017)
- [Global optimization of Lipschitz functions](https://mlsanity.com/paper/1703.02628/) (2017)
- [Accelerating Human-in-the-loop Machine Learning: Challenges and Opportunities](https://mlsanity.com/paper/1804.05892/) (2018)
- [Bayesian Optimization with Exponential Convergence](https://mlsanity.com/paper/1604.01348/) (2016)
- [Private Outsourced Bayesian Optimization](https://mlsanity.com/paper/2010.12799/) (2020)
- [Financial Applications of Gaussian Processes and Bayesian Optimization](https://mlsanity.com/paper/1903.04841/) (2019)
- [A sequential Monte Carlo approach to Thompson sampling for Bayesian optimization](https://mlsanity.com/paper/1604.00169/) (2016)
- [Regret Bounds for Gaussian-Process Optimization in Large Domains](https://mlsanity.com/paper/2104.14113/) (2021)
- [Optimistic optimization of a Brownian](https://mlsanity.com/paper/1901.04884/) (2019)

## Abstract (arXiv)

Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in sub-exponential time or be approximated within polynomial factor efficiently. We show that if a polynomial time algorithm can query informative Gaussian priors from an expert poly(n) times, then a class of combinatorial optimization problems can be solved efficiently in expectation up to a multiplicative factor ε where ε is arbitrary constant. While our proposed methods are merely theoretical, they cast new light on how to approach solving these problems that have been usually considered intractable.