Bayesian Binary Search
Vikash Singh, Matthew Khanzadeh, Vincent Davis, Harrison Rush,, Emanuele Rossi, Jesse Shrader, Pietro Lio
TL;DR
Bayesian Binary Search (BBS) introduces a probabilistic approach to binary search that uses learned probability densities to guide the search process, improving efficiency in simulated and real-world applications.
Contribution
The paper proposes Bayesian Binary Search, a novel probabilistic variant of binary search that incorporates machine learning to estimate search space densities and optimize the search process.
Findings
Significant efficiency improvements demonstrated on simulated data.
Effective application in real-world Bitcoin Lightning Network case.
Deployed successfully in a production environment.
Abstract
We present Bayesian Binary Search (BBS), a novel probabilistic variant of the classical binary search/bisection algorithm. BBS leverages machine learning/statistical techniques to estimate the probability density of the search space and modifies the bisection step to split based on probability density rather than the traditional midpoint, allowing for the learned distribution of the search space to guide the search algorithm. Search space density estimation can flexibly be performed using supervised probabilistic machine learning techniques (e.g., Gaussian process regression, Bayesian neural networks, quantile regression) or unsupervised learning algorithms (e.g., Gaussian mixture models, kernel density estimation (KDE), maximum likelihood estimation (MLE)). We demonstrate significant efficiency gains of using BBS on both simulated data across a variety of distributions and in a…
Peer Reviews
Decision·Submitted to ICLR 2025
The authors ask a good research question --- how we should perform binary search when the uniform distribution assumption does not hold.
Lack of baselines. The authors discuss many variants of binary search during introduction. However, none of them are used as baselines for comparison other than the classical binary search method. Plus, the proposed method described here is not very different from doing active learning using Gaussian Process. One more thing, doing density estimation can be time consuming. This could ultimately slow down the the search process and be much slower than the classical binary search method.
BBS is shown to improve efficiency in non-uniform search spaces, as evidenced by lower average steps to reach target values compared to standard binary search, especially in scenarios with a known or estimable distribution of search targets. The real-world example on the Lightning Network demonstrates a potential real-world use of the algorithm, if implemented appropriately.
There is nothing "Bayesian" about the proposed algorithm. Perhaps a more appropriate name would be "Probabilistic Binary Search". On the Lightning network experiment: The primary weakness of the experiment lies in a misalignment between the stated motivation for Bayesian Binary Search (BBS) and its actual implementation. - The experiment does not apply BBS to actual probing in the Lightning Network, where probing costs (in terms of network resources and latency) are the main concern. Instead,
Originality 1. Creatively combines classical binary search with probabilistic methods and introduces a flexible framework for incorporating various of PDF estimation methods 2. Provides a new perspective on search optimization through statistical learning Quality 1. Clear mathematical formulation and intuitive algorithm design 2. Rigorous analysis of robustness of BBS through KL divergence degradation simulation Clarity 1. The paper is well structured and the clarity is pretty good Significan
1. Lack the theoretic analysis of optimality of median split strategy 2. Lack theoretic analysis for convergence bounds with imperfect PDF estimation 3. The paper mentioned a few methods for PDF estimation (RF, GPR, BNN, etc.), however, only RF was used for the Bitcoin Lighting Network problem. Since PDF estimation is a crucial piece in the algorithm framework, it is necessary to offer comparative analysis among different PDF estimation approaches, as well as discussion of the trade-offs. 4. Sim
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Taxonomy
TopicsMetaheuristic Optimization Algorithms Research · Data Management and Algorithms · Bayesian Modeling and Causal Inference
MethodsGaussian Process