Treasure Search Optimization

Abstract

We introduce Treasure Search Optimization (TSO), an interacting particle method for global optimization. Most swarm methods balance exploration and exploitation within a single population, and typically switch between the two by degenerating the noise, annealing a temperature, or tuning a parameter. TSO instead splits these tasks across two kinds of agents. A swarm of explorers stays in exploration mode and a single treasure hunter performs exploitation. The hunter drifts toward an objective-weighted average of the explorers and may teleport to it when the move lowers the objective. The swarm then re-centers around the hunter, creating a feedback loop between search and capture. We model the dynamics as coupled jump-diffusion stochastic differential equations (SDEs). The hunter's jumps are shared by all explorers and act as a common noise. The mean-field limit is therefore a conditional McKean-Vlasov jump-diffusion SDE, whose well-posedness we prove. We also characterize the steady state and prove, via Laplace approximation techniques, that the hunter settles near the global minimum with error of order $1/α$, where $α$ is the weight parameter. Linking the consensus drift to a smoothed free energy, we explain why the swarm ignores spurious local traps and demonstrate how to quantify uncertainty in inverse problems using post-processing Kalman steps after TSO iterations. Numerical experiments on ODE-constrained problems and a low dimensional Bayesian inverse problem demonstrate the effectiveness of the TSO method.

Disclosure

“edish Research Council through grant agreement no. 2022-06725. I acknowledge the use of ChatGPT for help in code debugging and assistance in converting prototype code into the one used in numerical experiments. All outputs generated by the LLM were strictly manually reviewed and edited by me. I take full responsibility for the integrity of the code that it matches the methods, parameters, logical flow and and the resulting output as quoted in the paper. References [ABF+ 19]”

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Classification

Computational experiments or data processing

Multiplier

3

Verified

2026-08-23T18:57:19.543636Z

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