CVaR-RMD: CVaR Selection Pressure for Robust Metaheuristic Discovery

We study Bayesian optimization of the Conditional Value-at-Risk (CVaR) of an expensive black-box function that depends on a decision and an environmental variable. Existing no-regret algorithms assume that the correct Gaussian process (GP) kernel and its hyperparameters are known. In practice, however, they must be estimated from limited data, often yielding a misspecified surrogate. This is especially damaging for CVaR because misspecification can distort the estimated tail-risk and thus lead to catastrophic decisions. We propose HE-CV-UCB, the first no-regret algorithm for CVaR Bayesian optimization with unknown GP hyperparameters. Given a finite candidate set containing a well-specified model, HE-CV-UCB adaptively eliminates those inconsistent with the observed data, actively queries where the survivors disagree, and returns a design that is robust across the surviving candidates. We prove that it attains cumulative regret matching the oracle rate of CV-UCB up to a factor depending only on the candidate set's size. Across synthetic benchmarks and three real-world applications, HE-CV-UCB achieves competitive performance and frequently outperforms existing CVaR Bayesian optimization methods.

Automated Heuristic Design (AHD) with Large Language Models (LLMs) has shown remarkable progress in discovering high-quality heuristics. However, existing LLM-based AHD methods optimize heuristics for a fixed training instance set and may fail catastrophically when deployed under real-world distributional shifts. We propose Robust Adversary Instance Search (RAISE), a framework that integrates constrained worst-case instance search within a principled neighborhood of the training distribution into the LLM-based evolutionary search loop. RAISE treats robust AHD as a constrained adversarial instance search problem: the outer loop evolves heuristics via LLM operators, while an LLM-free inner loop efficiently identifies hard instances within an epsilon-ball around the training instance set using a basis distribution parameterization with boundary projection. Comprehensive experiments on Online Bin Packing (OBP), Online Job Shop Scheduling (OJSP), and Online Vehicle Routing (OVRP) across five distribution families demonstrate that existing LLM-based AHD methods degrade by up to 19 times under distribution shift, while RAISE consistently maintains strong performance across all tested distributions and problem scales

Large Language Model (LLM)-guided evolutionary search is increasingly used for automated algorithm discovery, yet most current methods track search progress primarily through executable programs and scalar fitness. Even when natural-language reasoning is used through heuristic descriptions or reflection, it typically remains transient mutation context or unstructured memory, rather than organized as persistent population-level state over strategic directions. As a result, evolutionary search can struggle to distinguish syntactically different implementations of the same idea, preserve lower-fitness but strategically promising directions, or detect when an entire family of strategies has saturated. We introduce \model, a modular strategy-space layer that turns language-level strategic reasoning into first-class population-level evolutionary state in LLM-driven program search. \model represents each candidate program with an explicit natural-language strategy, clusters the archive by strategy semantics, retrieves behaviorally complementary inspirations, and periodically navigates the strategy landscape to avoid saturated directions. Without modifying the underlying evolutionary algorithms, \model improves existing evolutionary backbones across algorithm discovery, systems optimization, and agent-scaffold design tasks in most settings. Across four systems benchmarks, \model achieves a 20.6% average relative improvement, with the best single run on Prism scoring 3$\times$ higher. These results suggest that persistent strategy representations provide a practical mechanism for improving the effectiveness and cost-efficiency of LLM-guided evolutionary search, pointing toward compound AI systems whose search capabilities benefit from the structured accumulation and reuse of algorithmic strategies.