OptScientist: Automated Discovery of Optimization Laws

What it claims

OptScientist recovers symbolic optimization laws (an objective plus inequality and equality constraints) from observational data without a pre-specified functional form. The 80% figure in the summary splits by outcome type. On the 99-problem OptFeynman benchmark, it achieves perfect exact-order recovery on 88 of 99 discrete problems and 78 of 99 continuous problems, on held-out contexts. On real data, it finds two specific laws. Human choice under risk and ambiguity is explained by expected reward plus a cognitive switching cost and a counterfactual reward term. Central-bank policy is explained by squared-error minimization toward a latent subjective target. The authors position it against inverse optimization, revealed preference and inverse RL, which estimate parameters of an optimization problem whose form is already assumed.

How it works

Any constrained law is rewritten as one scalar score S(x, y) using an exact-penalty reformulation (Han & Mangasarian, 1979). Hinge penalties handle inequality constraints and absolute-value penalties handle equality constraints. Noisy outcomes are modelled as p(y|x) ∝ exp(S/τ).

1. OptLearner uses the authors' earlier Behavior Learning Network as its backbone. Its early layers denoise and compress the inputs. A final single-block "optimization representation bottleneck" has learnable objective and constraint branches, scaled by λ0, λ1 and λ2. Discrete outcomes are trained with cross-entropy over all candidates. Continuous outcomes are trained with a contrastive loss against K sampled alternatives.
2. OptDiscover freezes OptLearner. It then fits a symbolic expression to each active branch by minimizing squared error against that branch's output. Symbolic regression therefore runs on the denoised, learned components rather than on raw data. An optional feature-extraction path handles inputs that are not already meaningful variables.

The agent wraps the model in an iterative loop:

flowchart LR
  A[Theory Prior Agent: priors, variables, hypotheses] --> B[Experiment Agent runs OptScientist Model]
  B --> C[Critic & Abstraction Agent]
  C -->|select, abstract law| D[Discovered law]
  C -->|suggest new variables or data| A

Evidence

OptFeynman is synthetic. It contains 99 optimization problems derived from analytic physics equations, with observations drawn as noisy samples from each induced landscape. The page reports that OptScientist "substantially" outperforms machine-learning, symbolic-regression and LLM model-discovery baselines on this benchmark. It also reports robustness when context variables are noisy. The fetched text does not name the baselines or give their scores.

On the risky-choice and monetary-policy data, the discovered laws are described as competitive with the strongest baselines on held-out prediction. They use near-minimal parameter counts and symbolic complexity, and fewer output tokens than LLM-based discovery methods. No numbers appear in the fetched portion for either domain.

Limits

The fetched text is cut off partway through Section 3. It contains no baseline tables, no compute or token figures, no named LLM, no code or data release, and no stated limitations. The real-world claims are relative ("competitive") with no metrics shown. OptFeynman is the authors' own synthetic benchmark. The backbone and related optimization-network work (Ma et al., 2026a/b) are also by the same first author. This is arXiv v1, dated 20 October 2026.