Though LLMs are capable of generating plausible programs, it's challenging to interact with the LLMs further to revise the program, especially if the user's specific requirements are different from the initial proposal.

The omnipresence of NP-hard combinatorial optimization problems (COPs) compels domain experts to engage in trial-and-error heuristic design. The long-standing endeavor of design automation has gained new momentum with the rise of large language models (LLMs).

Numerous real-world systems, ranging from healthcare to energy grids, involve users competing for finite and potentially scarce resources.

Designing effective algorithmic components remains a fundamental obstacle in tackling NP-hard combinatorial optimization problems (COPs), where solvers often rely on carefully hand-crafted strategies. Despite recent advances in using large language models (LLMs) to synthesize high-quality components, most approaches restrict the search to a single element - commonly a heuristic scoring function - thus missing broader opportunities for innovation. In this paper, we introduce a broader formulation of solver design as a multi-strategy optimization problem, which seeks to jointly improve a set of interdependent components under a unified objective. To address this, we propose Multi-strategy Optimization via Turn-based Interactive Framework (MOTIF) - a novel framework based on Monte Carlo Tree Search that facilitates turn-based optimization between two LLM agents. At each turn, an agent improves one component by leveraging the history of both its own and its opponent's prior updates, promoting both competitive pressure and emergent cooperation. This structured interaction broadens the search landscape and encourages the discovery of diverse, high-performing solutions. Experiments across multiple COP domains show that MOTIF consistently outperforms state-of-the-art methods, highlighting the promise of turn-based, multi-agent prompting for fully automated solver design.

Offline imitation learning (offline IL) enables training effective policies without requiring explicit reward annotations. Recent approaches attempt to estimate rewards for unlabeled datasets using a small set of expert demonstrations. However, these methods often assume that the similarity between a trajectory and an expert demonstration is positively correlated with the reward, which oversimplifies the underlying reward structure. We propose PROF, a novel framework that leverages large language models (LLMs) to generate and improve executable reward function codes from natural language descriptions and a single expert trajectory. We propose Reward Preference Ranking (RPR), a novel reward function quality assessment and ranking strategy without requiring environment interactions or RL training. RPR calculates the dominance scores of the reward functions, where higher scores indicate better alignment with expert preferences. By alternating between RPR and text-based gradient optimization, PROF fully automates the selection and refinement of optimal reward functions for downstream policy learning. Empirical results on D4RL demonstrate that PROF surpasses or matches recent strong baselines across numerous datasets and domains, highlighting the effectiveness of our approach.

Recent studies have suggested that Large Language Models (LLMs) could provide interesting ideas contributing to mathematical discovery. This claim was motivated by reports that LLM-based genetic algorithms produced heuristics offering new insights into the online bin packing problem under uniform and Weibull distributions. In this work, we reassess this claim through a detailed analysis of the heuristics produced by LLMs, examining both their behavior and interpretability. Despite being human-readable, these heuristics remain largely opaque even to domain experts. Building on this analysis, we propose a new class of algorithms tailored to these specific bin packing instances. The derived algorithms are significantly simpler, more efficient, more interpretable, and more generalizable, suggesting that the considered instances are themselves relatively simple. We then discuss the limitations of the claim regarding LLMs' contribution to this problem, which appears to rest on the mistaken assumption that the instances had previously been studied. Our findings instead emphasize the need for rigorous validation and con-textualization when assessing the scientific value of LLM-generated outputs.

Many high-stakes applications of AI require forming data-driven hypotheses and making targeted guesses; e.g., in scientific and diagnostic settings. Given limited resources, to what extent do agents based on language models (LMs) act rationally? We develop methods to benchmark and enhance agentic information-seeking, drawing on insights from human behavior. First, we introduce a strategic decision-oriented dialogue task called Collaborative Battleship, in which a partially-informed Captain must balance exploration (asking questions) and action (taking shots), while a fully-informed Spotter must provide accurate answers under an information bottleneck. Compared to human players (N=42), we find that LM agents struggle to ground answers in context, generate informative questions, and select high-value actions. Next, to address these gaps, we develop novel Monte Carlo inference strategies for LMs based on principles from Bayesian Experimental Design (BED). For Spotter agents, our approach boosts accuracy by up to 14.7% absolute over LM-only baselines; for Captain agents, it raises expected information gain (EIG) by up to 0.227 bits (94.2% of the achievable noise ceiling). Combined, these components yield sharper targeting (+0.303-0.374 F1), and enable weaker LMs, such as Llama-4-Scout, to outperform both humans (8% -> 82% win rate) and frontier models (0% -> 67% win rate vs. GPT-5) at ~1% of GPT-5's cost. We replicate these findings on Guess Who? where our methods significantly boost accuracy (+28.3-42.4 p.p.), demonstrating their general applicability for building rational information-seeking agents.

Classical models for supervised machine learning, such as decision trees, are efficient and interpretable predictors, but their quality is highly dependent on the particular choice of input features. Although neural networks can learn useful representations directly from raw data (e.g., images or text), this comes at the expense of interpretability and the need for specialized hardware to run them efficiently. In this paper, we explore a hypothesis class we call Learned Programmatic Representations (LeaPR) models, which stack arbitrary features represented as code (functions from data points to scalars) and decision tree predictors. We synthesize feature functions using Large Language Models (LLMs), which have rich prior knowledge in a wide range of domains and a remarkable ability to write code using existing domain-specific libraries. We propose two algorithms to learn LeaPR models from supervised data. First, we design an adaptation of FunSearch to learn features rather than directly generate predictors. Then, we develop a novel variant of the classical ID3 algorithm for decision tree learning, where new features are generated on demand when splitting leaf nodes. In experiments from chess position evaluation to image and text classification, our methods learn high-quality, neural network-free predictors often competitive with neural networks. Our work suggests a flexible paradigm for learning interpretable representations end-to-end where features and predictions can be readily inspected and understood.

The omnipresence of NP-hard combinatorial optimization problems (COPs) compels domain experts to engage in trial-and-error heuristic design. The long-standing endeavor of design automation has gained new momentum with the rise of large language models (LLMs).

Though LLMs are capable of generating plausible programs, it's challenging to interact with the LLMs further to revise the program, especially if the user's specific requirements are different from the initial proposal.