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Zuyuan Zhang

Zuyuan Zhang contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence

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preprint2026arXiv

Interactive Critique-Revision Training for Reliable Structured LLM Generation

In structured decision-making workflows such as form filling, compliance checking, and maintenance reporting, LLM outputs must be locally correct, globally consistent, and auditable against task-specific rules. Existing refinement methods often rely on heuristic debate, self-play, or LLM-generated supervision, creating a second-order assurance problem. We propose DPA-GRPO (Dual Paired-Action Group-Relative Policy Optimization), a paired-action training method for a two-player generator--verifier game with structured verifier interventions. The generator proposes outputs and may revise them when challenged; the verifier either remains silent or raises a safety assurance case (SAC) containing a claim, argument, and evidence. These SAC/no-SAC and KEEP/REVISE decisions induce paired counterfactual action groups, which DPA-GRPO uses for role-specific KL-regularized GRPO updates. We analyze the unregularized game and show that positive probability on strictly lower-reward intervention or revision actions creates a profitable unilateral deviation. Under standard stochastic-approximation assumptions, DPA-GRPO tracks the corresponding game ODE, whose isolated asymptotically stable limit points are stationary and candidate local equilibria under role-wise local optimality. Experiments on TaxCalcBench TY24 show that DPA-GRPO improves structured decision accuracy over zero-shot generation and generator-only RL baselines across Qwen3-4B and Qwen3-8B. Training increases correct silent acceptance, reduces missed errors, and improves calibrated revision behavior, indicating gains for both generator and verifier.

preprint2026arXiv

Matrix-Space Reinforcement Learning for Reusing Local Transition Geometry

Compositional generalization in sequential decision-making requires identifying which parts of prior rollouts remain useful for new tasks. Existing methods reuse skills or predictive models, but often overlook rich local transition geometry and dynamics. We propose Matrix-Space Reinforcement Learning (MSRL), a geometric abstraction that represents trajectory segments through positive semidefinite matrix descriptors aggregating first- and second-order statistics of lifted one-step transitions. These descriptors expose shared hidden structure, support algebraic composition in an abstract matrix space, and reveal opportunities for transfer. We prove that the descriptor is well defined up to coordinate gauge, complete for the induced low-order additive signal class, additive under valid segment composition, and minimally sufficient among admissible additive descriptors. We further show that conditioning value functions on the trajectory-segment matrix yields a first-order smooth approximation of action values, enabling source-learned matrix-to-value mappings to bootstrap learning in new tasks. MSRL is plug-in compatible with standard model-free and model-based methods, while obstruction filtering rejects implausible compositions. Empirically, MSRL achieves the best average finite-budget target AUC of 0.73, outperforming MSRL from scratch (0.65), TD-MPC-PT+FT (0.63), and TD-MPC (0.57).

preprint2026arXiv

Metric-Gradient Projection for Stable Multi-Agent Policy Learning

General-sum multi-agent learning is often governed by a stacked update field in which each agent's policy update changes the optimization landscape faced by the others. This coupling can entangle an integrable component of collective improvement with cyclic interaction dynamics, leading to slow or unstable multi-agent learning. Existing approaches, such as regularization, credit assignment, and consensus methods, stabilize MARL through local or algorithmic modifications; HPML complements them by projecting the joint update field onto a metric-gradient component. We introduce \textbf{HPML} (\textbf{H}odge-\textbf{P}rojected \textbf{M}ulti-agent \textbf{L}earning), which views the joint update field of a multi-agent system as an element of an $L^2$ space of vector fields and computes a Hodge-type projection onto the closest metric-gradient potential flow. HPML follows the projected component as the update direction, yielding the closest metric-gradient field under the chosen metric and sampling measure. The projection is defined variationally, characterized by a Poisson-type equation, and implemented through graph-based and amortized neural realizations that recover projected directions from samples. We show that the projected dynamics admit a Lyapunov potential and yield equilibrium-gap bounds with an explicit additive non-potentiality term. Controlled experiments validate the geometric mechanism, and CTDE benchmarks show improved stability and normalized return when HPML is used as a plug-in projection layer in MARL pipelines.

preprint2026arXiv

NonZero: Interaction-Guided Exploration for Multi-Agent Monte Carlo Tree Search

Monte Carlo Tree Search (MCTS) scales poorly in cooperative multi-agent domains because expansion must consider an exponentially large set of joint actions, severely limiting exploration under realistic search budgets. We propose NonZero, which keeps multi-agent MCTS tractable by running surrogate-guided selection over a low-dimensional nonlinear representation using an interaction-guided proposal rule, instead of directly exploring the full joint-action space. Our exploration uses an interaction score: single-agent deviations are ranked by predicted gain, while two-agent deviations are scored by a mixed-difference measure that reveals coordination benefits even when no single agent can improve alone. We formalize candidate proposal as a bandit problem over local deviations and derive a proposal rule, NonZero, with a sublinear local-regret guarantee for reaching approximate graph-local optima without enumerating the joint-action space. Empirically, NonZero improves sample efficiency and final performance on MatGame, SMAC, and SMACv2 relative to strong model-based and model-free baselines under matched search budgets.

preprint2026arXiv

Operator-Guided Invariance Learning for Continuous Reinforcement Learning

Reinforcement learning (RL) with continuous time and state/action spaces is often data-intensive and brittle under nuisance variability and shift, motivating methods that exploit value-preserving structures to stabilize and improve learning. Most existing approaches focus on special cases, such as prescribed symmetries and exact equivariance, without addressing how to discover more general structures that require nonlinear operators to transform and map between continuous state/action systems with isomorphic value functions. We propose \textbf{VPSD-RL} (Value-Preserving Structure Discovery for Reinforcement Learning). It models continuous RL as a controlled diffusion with value-preserving mappings defined through Lie-group actions and associated pullback operators. We show that a value-preserving structure exists exactly when pulling back the value function and pushing forward actions commute with the controlled generator and reward functional. Further, approximate value-preserving structures with rigorous guarantees can be found when the Hamilton--Jacobi--Bellman mismatch is small. This framework discovers exact and approximate value-preserving structures by searching for the associated Lie group operators. VPSD-RL fits differentiable drift, diffusion, and reward models; learns infinitesimal generators via determining-equation residual minimization; exponentiates them with ODE flows to obtain finite transformations; and integrates them into continuous RL through transition augmentation and transformation-consistency regularization. We show that bounded generator/reward mismatch implies quantitative stability of the optimal value function along approximate orbits, with sensitivity governed by the effective horizon, and observe improved data efficiency and robustness on continuous-control benchmarks.

preprint2026arXiv

Second-Order Convergence in Private Stochastic Non-Convex Optimization

We investigate the problem of finding second-order stationary points (SOSP) in differentially private (DP) stochastic non-convex optimization. Existing methods suffer from two key limitations: (i) inaccurate convergence error rate due to overlooking gradient variance in the saddle point escape analysis, and (ii) dependence on auxiliary private model selection procedures for identifying DP-SOSP, which can significantly impair utility, particularly in distributed settings. To address these issues, we propose a generic perturbed stochastic gradient descent (PSGD) framework built upon Gaussian noise injection and general gradient oracles. A core innovation of our framework is using model drift distance to determine whether PSGD escapes saddle points, ensuring convergence to approximate local minima without relying on second-order information or additional DP-SOSP identification. By leveraging the adaptive DP-SPIDER estimator as a specific gradient oracle, we develop a new DP algorithm that rectifies the convergence error rates reported in prior work. We further extend this algorithm to distributed learning with heterogeneous data, providing the first formal guarantees for finding DP-SOSP in such settings. Our analysis also highlights the detrimental impacts of private selection procedures in distributed learning under high-dimensional models, underscoring the practical benefits of our design. Numerical experiments on real-world datasets validate the efficacy of our approach.

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