InvEvolve: Evolving White-Box Inventory Policies via Large Language Models with Performance Guarantees

Firms making inventory decisions have access to operational data, optimization tools, and large language models (LLMs). Typically, data characterize the operating environment, optimization selects parameters within a prespecified inventory policy class, and LLMs support coding and decision analysis. We develop an integrated framework that combines these resources to automate inventory policy design. Given demand data, the framework iteratively uses an LLM to generate parameterized policy classes and an external solver to optimize its parameters within each class. Across 30 lost-sales inventory instances, the mean cost reduction relative to optimized base-stock benchmarks increases from 17.5% after one generation to 30.0% after ten generations. Parameter optimization is central to this performance: an LLM-only variant performs substantially worse, whereas optimization-guided feedback improves policy quality, accelerates search, and directs the LLM toward better policy classes rather than merely better parameter values within a fixed class. The strongest discovered policies are also interpretable: they combine recognizable inventory-control motifs, including capped orders, discounted or weighted pipeline inventory, and threshold-based replenishment logic. The search thereby produces new policy-class functional forms that, to our knowledge, have not previously been studied in the lost-sales inventory literature. These functional forms are not specified ex ante but emerge from the search process. Moreover, after their parameters are re-optimized, three discovered policy classes achieve average cost reductions of 21.75% to 22.60% across 10,064 new inventory instances. Overall, the results show that data-driven parameter optimization can guide LLM-based search over a broad space of inventory policy classes and identify high-performing, interpretable, and transferable decision rules.

Inventory-policy comparisons are often difficult to interpret because performance depends on the evaluation contract as much as on the policy itself. Differences in topology, demand regime, information access, feasibility constraints, shortage treatment, and Key Performance Indicator (KPI) definitions can change method rankings. We present gym-invmgmt, a Gymnasium-compatible extension of the OR-Gym inventory-management lineage for auditable cross-paradigm evaluation. The benchmark evaluates optimization, heuristic, and learned controllers under a shared CoreEnv transition, reward, action-bound, and KPI contract, while varying stress conditions through a 22-scenario core grid plus four supplemental MARL-mode rows. Within these released scenarios, informed stochastic programming provides the strongest non-oracle reference, reflecting the value of scenario hedging under forecast access, but at substantially higher online computational cost. Among learned controllers, the Proximal Policy Optimization Transformer variant (PPO-Transformer) achieves the strongest learned-policy quality at fast inference, while Residual Reinforcement Learning (Residual RL) provides competitive hybrid performance. The graph neural network variant (PPO-GNN) is highly competitive on the default divergent topology but less robust on the serial topology. Imitation learning performs well in stationary regimes but degrades under demand shift, and the bounded Large Language Model (LLM) policy-parameter baseline is best interpreted as a diagnostic controller rather than an autonomous inventory optimizer. Overall, the benchmark identifies scenario-conditioned leaders while showing that performance depends jointly on information access, demand shift, topology, and policy representation.

Autonomous LLM training is often framed as recipe search, which leaves the training harness largely static. This limitation sharpens in agentic RL, where shifting bottlenecks and scalar rewards mask diverse failure modes. We introduce EvoTrainer, an autonomous training framework that co-evolves LLM policies and training-side harnesses through empirical feedback: it diagnoses rollout-level evidence, revises diagnostics, backtests interventions, and accumulates reusable skills. Evaluated on mathematical reasoning, competitive-programming code generation, and repository-level software engineering, EvoTrainer matches or exceeds the human-engineered RL references under the same data, codebase, and evaluation protocol, with the largest gain on long-horizon agentic SWE. Trajectory analyses show that retained strategies diverge across domains, evolving diagnostics prevent invalid high-scoring branches from being promoted, and reusable skills shape later search. Autonomous LLM RL should move beyond recipe search toward joint evolution of policies and the training harnesses that interpret them.