Lei Yuan
Publications
Efficient Test-Time Optimization for Multi-Agent Proof Autoformalization
Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning. Unlike statement-level formalization, proof autoformalization is a long-horizon challenge requiring coordination of claims, contexts, and dependencies across many proof steps, yet has only recently come under focused study. Current approaches either rely on costly model training or apply excessive, unguided repair at inference time. To this end, we introduce ToMap, a multi-agent framework that structures proof autoformalization as a Decomposer-Formalizer-Prover pipeline with efficient test-time optimization guided by formal verification and semantic rubrics for proof quality. Rather than distributing test-time compute across all agents, we perform bottleneck analysis and identify the Decomposer as the critical bottleneck: the quality of its atomic, self-contained proof units directly determines whether downstream agents can successfully formalize and prove each step. ToMap therefore treats the Formalizer and Prover as downstream executors and efficiently focuses test-time compute on Decomposer refinement. This refinement follows a loop inspired by GEPA, evolving prompts over candidate decompositions and using formal verification progress together with semantic proof rubrics to define a Pareto frontier that guides the next decomposition update. Experiments on ProofFlowBench show that ToMap improves over the best previous method by 19.0% when evaluated by both syntactic correctness and semantic faithfulness, while requiring lower test-time cost. Scaling analysis shows that most gains emerge within a few iterations of decomposition evolution, guiding test-time budget selection.
Offline Multi-agent Continual Cooperation via Skill Partition and Reuse
Extracting skills from multi-agent offline dataset improves learning efficiency via sharing task-invariant coordination skills among tasks. In settings where tasks occur sequentially and the space of skills grows exponentially, existing approaches that rely on heuristically designed and fixed-sized skill libraries struggle to resolve the problem of distributional shift and interference, facing catastrophic forgetting and plasticity loss. To address this problem and endow agents with the ability to continually discover and reuse coordination skills in open-environment, we propose COMAD, a principled framework for Continual Offline Multi-agent Skill Discovery via Skill Partition and Reuse. We first discover skills from mixed multi-agent behavior data with an auto-encoder to transform coordination knowledge into reusable coordination skills. Then we construct a skill-augmented policy learning objective with multi-head architectures, explicitly guiding the advantage function with reusable skills identified via a density-based reusability estimator. Theoretical analysis shows our method approximates the optimum of a continual skill discovery problem. Empirical results across diverse MARL benchmarks show that COMAD continually expands its skill library to mitigate interference, achieving superior forward and backward transfer for task streams compared to multiple baselines.
Model-Based Proactive Cost Generation for Learning Safe Policies Offline with Limited Violation Data
Learning constraint-satisfying policies from offline data without risky online interaction is crucial for safety-critical decision making. Conventional methods typically learn cost value functions from abundant unsafe samples to define safety boundaries and penalize violations. However, in high-stakes scenarios, risky trial-and-error is infeasible, yielding datasets with few or no unsafe samples. Under this limitation, existing approaches often treat all data as uniformly safe, overlooking safe-but-infeasible states - states that currently satisfy constraints but inevitably violate them within a few steps - leading to deployment failures. Drawing inspiration from the concept of knowledge-data integration, we leverage large language models (LLMs) to incorporate natural language knowledge into the policy to address this challenge. Specifically, we propose PROCO, a model-based offline safe reinforcement learning (RL) framework tailored to datasets largely free of violations. PROCO first learns a dynamics model from offline data and constructs a conservative cost function by grounding natural-language knowledge of unsafe states in LLMs, enabling risk estimation even without observed violations. Using the cost function and learned model, PROCO performs model-based rollouts to synthesize diverse counterfactual unsafe samples, supporting reliable feasibility identification and feasibility-guided policy learning. Across a range of Safety-Gymnasium tasks with exclusively safe or minimally risky training data, PROCO integrates seamlessly with a variety of offline safe RL algorithms and consistently demonstrates reduced constraint violations and improved safety performance compared to both the original methods and other behavior cloning baselines.