Fei Xu Yu

Yu Li, Sizhe Tang, Rongqian Chen et al.

Automated cyber defense (ACD) seeks to protect computer networks with minimal or no human intervention, reacting to intrusions by taking corrective actions such as isolating hosts, resetting services, deploying decoys, or updating access controls. However, existing approaches for ACD, such as deep reinforcement learning (RL), often face difficult exploration in complex networks with large decision/state spaces and thus require an expensive amount of samples. Inspired by the need to learn sample-efficient defense policies, we frame ACD in CAGE Challenge 4 (CAGE-4 / CC4) as a context-based partially observable Markov decision problem and propose a planning-centric defense policy based on Monte Carlo Tree Search (MCTS). It explicitly models the exploration-exploitation tradeoff in ACD and uses statistical sampling to guide exploration and decision making. We make novel use of graph neural networks (GNNs) to embed observations from the network as attributed graphs, to enable permutation-invariant reasoning over hosts and their relationships. To make our solution practical in complex search spaces, we guide MCTS with learned graph embeddings and priors over graph-edit actions, combining model-free generalization and policy distillation with look-ahead planning. We evaluate the resulting agent on CC4 scenarios involving diverse network structures and adversary behaviors, and show that our search-guided, graph-embedding-based planning improves defense reward and robustness relative to state-of-the-art RL baselines.

Zuyuan Zhang, Fei Xu Yu, Tian Lan

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.

Fei Xu Yu, Zuyuan Zhang, Mahdi Imani et al.

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.

Fei Xu Yu, Gina Adam, Nathaniel D. Bastian et al.

Large language models (LLMs) have demonstrated remarkable capabilities in code generation and structured reasoning; however, their performance often degrades on complex tasks that require consistent multi-step planning. Recent work has explored combining LLMs with Monte Carlo Tree Search (MCTS), yet existing approaches primarily focus on generating heuristic-based code for optimization or target simpler tasks where correctness alone is sufficient. In this work, we propose MCTS-OPS, a novel neural-symbolic framework that formulates prompt selection as a sequential decision process guided by MCTS. Our method explores and refines multi-step prompt sequences for the goal of improving code generation quality and enhancing the problem-solving capabilities of LLMs in general optimization. Experiments on network optimization show significant improvement over the baselines, both in the success rate of executing the generated code and in the optimization results with the specified objective and constraints (2$\sim$4$\times$ higher reward and 3$\times$ lower standard deviation). Moreover, it improves the chance of attaining the optimal solution by about 10\% of cases, compared to baseline methods in hard problems. These results highlight the promise of combining symbolic planning with LLMs for robust, high-quality code generation in complex domains.