Qingsong Ran

Zhongzheng Li, Tiancan Feng, Wenhao Li et al.

Designing optimizers for modern deep learning remains a challenging scientific problem, requiring the joint consideration of optimization geometry, state dynamics, numerical stability, implementation constraints, and empirical generalization. Existing automated optimizer discovery methods typically search either over unconstrained code spaces or within narrowly parameterized optimizer families. The former is flexible but often produces invalid or uninterpretable programs, while the latter is stable but limits novelty. We introduce OPTScientist, a theory-guided multi-agent framework for optimizer discovery in a typed domain-specific language (DSL). OPTScientist formulates optimizer design as a constrained scientific search process, where candidate updates are expressed through direction, scaling, preconditioning, regularization, state, and grouping modules. Four role agents, Theorist, Designer, Engineer, and Reviewer, collaborate within a single orchestration loop to propose hypotheses, synthesize DSL candidates, compile and evaluate optimizers, and critique results. To overcome the limitations of a fixed search space, OPTScientist combines evolutionary search over optimizer programs with a second-stage mechanism that proposes small DSL extensions when repeated failures reveal representational bottlenecks. Using this framework, we discover RS-MR, a reduced-state matrix optimizer that improves transformer pretraining over strong baselines under our native evaluation protocol. Our results suggest a path toward automated optimizer science grounded in theory, typed programs, compiler validation, and closed-loop experimentation.

Nian Ran, Zhongzheng Li, Yue Wang et al.

Multi-objective discrete optimization problems, such as molecular design, pose significant challenges due to their vast and unstructured combinatorial spaces. Traditional evolutionary algorithms often get trapped in local optima, while expert knowledge can provide crucial guidance for accelerating convergence. Large language models (LLMs) offer powerful priors and reasoning ability, making them natural optimizers when expert knowledge matters. However, closed-source LLMs, though strong in exploration, cannot update their parameters and thus cannot internalize experience. Conversely, smaller open models can be continually fine-tuned but lack broad knowledge and reasoning strength. We introduce Multi-LLM Collaborative Co-evolution (MCCE), a hybrid framework that unites a frozen closed-source LLM with a lightweight trainable model. The system maintains a trajectory memory of past search processes; the small model is progressively refined via reinforcement learning, with the two models jointly supporting and complementing each other in global exploration. Unlike model distillation, this process enhances the capabilities of both models through mutual inspiration. Experiments on multi-objective drug design benchmarks show that MCCE achieves state-of-the-art Pareto front quality and consistently outperforms baselines. These results highlight a new paradigm for enabling continual evolution in hybrid LLM systems, combining knowledge-driven exploration with experience-driven learning.