Bandits attack function optimization

TL;DR

This paper introduces SOO, a deterministic bandit-inspired algorithm for function optimization that balances exploration and exploitation under evaluation budget constraints, with proven guarantees and empirical validation.

Contribution

The paper proposes the novel SOO algorithm, combining domain partitioning with bandit principles, offering theoretical guarantees and empirical performance in optimization tasks.

Findings

SOO effectively balances exploration and exploitation.

The algorithm provides guarantees on solution quality.

Empirical results show competitive performance on benchmark tests.

Abstract

We consider function optimization as a sequential decision making problem under budget constraint. This constraint limits the number of objective function evaluations allowed during the optimization. We consider an algorithm inspired by a continuous version of a multi-armed bandit problem which attacks this optimization problem by solving the tradeoff between exploration (initial quasi-uniform search of the domain) and exploitation (local optimization around the potentially global maxima). We introduce the so-called Simultaneous Optimistic Optimization (SOO), a deterministic algorithm that works by domain partitioning. The benefit of such approach are the guarantees on the returned solution and the numerical efficiency of the algorithm. We present this machine learning approach to optimization, and provide the empirical assessment of SOO on the CEC'2014 competition on single objective real-parameter numerical optimization test-suite.