Abstract
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.