An LP-based hyperparameter optimization model for language modeling

TL;DR

This paper introduces a novel LP-based optimization model for hyperparameter tuning in language models, specifically targeting perplexity minimization, and demonstrates its effectiveness over traditional grid search on real-world data.

Contribution

It presents the first optimization-based approach for directly finding optimal perplexity values in language modeling, using a linear programming approximation.

Findings

The LP-based method achieves lower perplexity than grid search.

The approach is validated on a real-world dataset from SwiftKey.

It offers a new optimization perspective for hyperparameter tuning.

Abstract

In order to find hyperparameters for a machine learning model, algorithms such as grid search or random search are used over the space of possible values of the models hyperparameters. These search algorithms opt the solution that minimizes a specific cost function. In language models, perplexity is one of the most popular cost functions. In this study, we propose a fractional nonlinear programming model that finds the optimal perplexity value. The special structure of the model allows us to approximate it by a linear programming model that can be solved using the well-known simplex algorithm. To the best of our knowledge, this is the first attempt to use optimization techniques to find perplexity values in the language modeling literature. We apply our model to find hyperparameters of a language model and compare it to the grid search algorithm. Furthermore, we illustrating that it results in lower perplexity values. We perform this experiment on a real-world dataset from SwiftKey to validate our proposed approach.