Scientific discovery as meta-optimization: a combinatorial optimization case study

Scientific discovery is often hindered by the difficulty of defining precise, stable objectives, leading to reward hacking where systems optimize for flawed metrics. The authors propose a meta-optimization framework where both the research solutions and the evaluation criteria evolve simultaneously. The system employs a multi-agent architecture—comprising a meta-agent, objective agent, planner, and designer—to iterate through research cycles. Central to this is "consensus objective aggregation," which maintains a portfolio of proxy objectives and combines them using correlation-weighted voting. This mechanism suppresses outlier objectives and uses age decay to ensure the evaluation criteria evolve as the system gains a deeper understanding of the research problem.

Rather than relying on a single, potentially misleading proxy, the framework generates multiple objectives that capture different facets of solution quality. These are aggregated using Kendall’s tau rank correlations to identify objectives that agree with the majority, which are then weighted more heavily. A meta-agent provides top-down guidance to prevent "echo chambers" where redundant objectives dominate. This self-correcting process allows the research goal to shift from simple initial heuristics to more sophisticated, large-scale performance metrics as the search progresses.

The authors applied this framework to discover efficient algorithms for 3-SAT problems using digital MemComputing machines (DMMs). By exploring 414 solver designs guided by 42 co-evolving objectives, the system identified a solver that significantly outperforms the baseline. The best design reduced the scaling exponent from N^2.51 to N^1.33, demonstrating the efficacy of the meta-optimization approach in complex combinatorial spaces. The framework's use of multi-fidelity execution allowed the system to allocate computational resources efficiently, focusing on the most promising candidates.