Self-improving agents accumulate capability by repeatedly rewriting procedural policies, controllers, or heuristic rules. They typically rely on self-authored tests or metrics to decide whether to accept subsequent edits. The agent controls both the optimized object and its verifier. As a result, self-assigned scores can remain near perfect while real deployment performance degrades or stays low. We study this problem through the verifier--deployment gap. This gap refers to the discrepancy between an agent's self-authored verification signal and a sealed deployment evaluation that the agent cannot observe or access. We ask how self-authored verification fails under iterative policy-and-test rewriting, how the failure changes with capability, and how little exogenous trust is sufficient to prevent real regressions from being deployed. To address this problem, we introduce a Sealed Exogenous Acceptance Loop (SEAL). SEAL retains self-authored tests but compares each candidate with the incumbent through a fixed harness-side audit. The agent cannot author or inspect the audit, receives only accept/reject, and the whole incumbent state is retained after a clear regression. Our experiments show that this problem often appears in heuristic learning settings. These settings require trial-and-error discovery of the target objective. We further find that failures of self-written verification are stratified by capability. Weaker agents tend to damage previously acquired strategies behind easy self-tests. Stronger agents are more stable, but they still mismeasure the deployment distribution. Standard self-written constraints do not reliably close this gap. In contrast, SEAL outperforms unprotected baselines across six models and three random seeds. Reliable self-improvement need not abandon self-verification, but it requires at least one deployment-acceptance signal outside the agent's control.
Lean 4's grind tactic combines congruence closure, E-matching, and case-splitting into a single automated solver, and like any such solver, it relies on hand-tuned heuristics to decide what to instantiate and where to case-split. These heuristics are tempting targets for learning, but there is a catch: because grind's search is non-monotone, a learned heuristic that helps one proof can break another, and an always-on replacement usually nets out near zero. We avoid this by invoking a learned intervention only after stock grind has already failed: a failure-triggered cascade that, by construction, cannot lose a proof grind already had. We apply it to two of grind's internal decisions. A cost-aware E-matching filter solves slightly more problems and runs about 5% faster. A lookahead step proves five theorems it otherwise times out on. We also report the negative result that motivated the design: across four feature-based models, statically predicting the correct case split is no better than random, because whether a split explodes is a runtime property that the features do not capture. Our results suggest that learning within theorem-proving tactics is most effective as a mechanism for deciding when and how to spend bounded search, backed by a reliable symbolic fallback.
Paul Garnier, Jonathan Viquerat, Elie Hachemcs.LG cs.AI physics.flu-dyn
Active flow control involves nonlinear dynamics, partial observations, and computationally expensive simulations, making controller design particularly challenging. Deep reinforcement learning (DRL) has emerged as a powerful framework for such problems, but its success typically relies on large numbers of simulator interactions and produces neural-network policies whose decision process often remains difficult to interpret. In this work, we investigate a different paradigm: instead of optimizing neural-network parameters, we use modern coding agents to search directly for explicit executable feedback laws. We introduce a constrained heuristic-learning protocol in which an agent iteratively proposes, evaluates, and revises controller implementations while interacting exclusively through the public benchmark interface. The proposed framework is evaluated on 13 active flow-control benchmarks spanning one, two, and three-dimensional problems and compared against the strongest available DRL baselines under identical simulation budgets. The discovered heuristic controllers match or outperform the best DRL policy in 10 of the 13 environments while remaining compact, interpretable, and directly inspectable. Beyond aggregate performance, the resulting controllers reveal physically meaningful feedback mechanisms, transfer successfully across more challenging configurations, and remain competitive under varying Reynolds and Rayleigh numbers, actuator counts, and observation sparsity. These results suggest that heuristic learning through coding agents constitutes a credible and complementary alternative to conventional reinforcement learning, combining competitive performance with physically interpretable controller representations. Prompts and source code are available at https://github.com/DonsetPG/fluid-heuristic-learning.
String constraint solvers are crucial for reasoning about string-manipulating programs. However, many practical string constraints are undecidable, and real-world applications often present complex constraints that challenge current solvers. The rise of multi-core architectures offers an opportunity for parallel solving. A key parallel solving method is \emph{cube-and-conquer}, in which the quality of splitting heuristics is critical to effectively dividing the search space. Unfortunately, manually designing the heuristics is labor-intensive, and handcrafted heuristics are often sub-optimal. This paper introduces a data-driven approach to automatically generating splitting heuristics. We frame the problem of selecting a splitting atom as a learning task, using features from input formulas and dynamic data from solver execution. We implement this approach in two popular string solvers, Z3seq and Z3str4, demonstrating that the learned heuristics outperform manually designed ones in the number of solved formulas and the average solving time.