Budget-Efficient Automatic Algorithm Design via Code Graph
Maxime Bouscary, Manxi Wu, Saurabh Amin

TL;DR
This paper introduces a budget-efficient method for automatic algorithm design using a graph-based approach that leverages LLMs to generate and refine algorithms through corrections, improving search efficiency.
Contribution
It formalizes a graph representation of algorithms and a correction-based search framework that enhances efficiency over traditional full-algorithm queries.
Findings
Graph-based search outperforms full-algorithm search at equal token budgets.
Corrections enable more efficient exploration of algorithm space.
Rich context helps mainly when LLM's prior knowledge is shallow.
Abstract
Large language models (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring substructures and discarding low-fitness candidates that may contain valuable algorithmic features. We formalize budget-efficient automatic algorithm design, wherein the search policy maximizes realized fitness subject to limited computational cost. We propose a directed acyclic graph representation of algorithms and build a search framework that fully exploits the LLM's output. Instead of querying the LLM for full algorithms, we use it to obtain corrections: compact operators that add, replace, or remove code blocks. Each correction augments the graph, yielding new algorithms that compose with prior corrections. This graph structure decomposes algorithms into…
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