Optimal Stopping of Self-Refining Foundation Models

Foundation models can improve their outputs through a self-refinement process driven by external feedback. In this process, the model is embedded in an iterative loop where it generates outputs, receives feedback from verifiers, and refines its responses through in-context learning. Following a novel approach, we formalize this process as an optimal stopping problem where the number of refinement iterations is decided based on expected improvement relative to cost. We derive optimal stopping policies and show that they can be efficiently computed through stochastic approximation. To evaluate our approach experimentally, we apply it to a coding benchmark for foundation models. The empirical results show that our stopping policies are significantly more cost-efficient than stopping policies proposed in prior work.

Agentic Incident Response through Digital Twin-Enhanced Multiscale Planning

Incident response is currently managed by security operators using predefined playbooks, resulting in slow, labor-intensive security decision-making processes. Consequently, there is a growing need for automated incident response planning. Decision-theoretic approaches based on control, optimization, and reinforcement learning have been proposed to automate such planning tasks with well-grounded approaches, yet most of which, while guaranteeing strong performance, are limited to abstract models and cannot be directly applied to operational systems. A promising approach to mitigate this limitation is to use the security knowledge embedded in large language models (LLMs) to develop agentic response systems. However, current agentic approaches rely on repeated invocations of the LLM to generate a response plan, which is unreliable and limits the planning horizon due to hallucination. In this paper, we develop a principled LLM-based planning method by combining decision-theoretic planning with LLM-generated response commands. The proposed agentic incident response approach uses a rollout planner to compute a high-level response strategy that allocates security resources (the tactical scale), which is then translated into executable commands by a lightweight LLM agent (the operational scale). Within this architecture, we use a digital twin that supports tactical planning through simulation and operational execution through emulation. Across three attack scenarios, our agentic approach reduces recovery execution time by 15.1\% on average and increases the recovery rate by 33.6\% over frontier LLM baselines.

In-Context Autonomous Network Incident Response: An End-to-End Large Language Model Agent Approach

Rapidly evolving cyberattacks demand incident response systems that can autonomously learn and adapt to changing threats. Prior work has extensively explored the reinforcement learning approach, which involves learning response strategies through extensive simulation of the incident. While this approach can be effective, it requires handcrafted modeling of the simulator and suppresses useful semantics from raw system logs and alerts. To address these limitations, we propose to leverage large language models' (LLM) pre-trained security knowledge and in-context learning to create an end-to-end agentic solution for incident response planning. Specifically, our agent integrates four functionalities, perception, reasoning, planning, and action, into one lightweight LLM (14b model). Through fine-tuning and chain-of-thought reasoning, our LLM agent is capable of processing system logs and inferring the underlying network state (perception), updating its conjecture of attack models (reasoning), simulating consequences under different response strategies (planning), and generating an effective response (action). By comparing LLM-simulated outcomes with actual observations, the LLM agent repeatedly refines its attack conjecture and corresponding response, thereby demonstrating in-context adaptation. Our agentic approach is free of modeling and can run on commodity hardware. When evaluated on incident logs reported in the literature, our agent achieves recovery up to 23% faster than those of frontier LLMs.

Hallucination-Resistant Security Planning with a Large Language Model

Large language models (LLMs) are promising tools for supporting security management tasks, such as incident response planning. However, their unreliability and tendency to hallucinate remain significant challenges. In this paper, we address these challenges by introducing a principled framework for using an LLM as decision support in security management. Our framework integrates the LLM in an iterative loop where it generates candidate actions that are checked for consistency with system constraints and lookahead predictions. When consistency is low, we abstain from the generated actions and instead collect external feedback, e.g., by evaluating actions in a digital twin. This feedback is then used to refine the candidate actions through in-context learning (ICL). We prove that this design allows to control the hallucination risk by tuning the consistency threshold. Moreover, we establish a bound on the regret of ICL under certain assumptions. To evaluate our framework, we apply it to an incident response use case where the goal is to generate a response and recovery plan based on system logs. Experiments on four public datasets show that our framework reduces recovery times by up to 30% compared to frontier LLMs.

Online Incident Response Planning under Model Misspecification through Bayesian Learning and Belief Quantization

Effective responses to cyberattacks require fast decisions, even when information about the attack is incomplete or inaccurate. However, most decision-support frameworks for incident response rely on a detailed system model that describes the incident, which restricts their practical utility. In this paper, we address this limitation and present an online method for incident response planning under model misspecification, which we call MOBAL: Misspecified Online Bayesian Learning. MOBAL iteratively refines a conjecture about the model through Bayesian learning as new information becomes available, which facilitates model adaptation as the incident unfolds. To determine effective responses online, we quantize the conjectured model into a finite Markov model, which enables efficient response planning through dynamic programming. We prove that Bayesian learning is asymptotically consistent with respect to the information feedback. Additionally, we establish bounds on misspecification and quantization errors. Experiments on the CAGE-2 benchmark show that MOBAL outperforms the state of the art in terms of adaptability and robustness to model misspecification.

Incident Response Planning Using a Lightweight Large Language Model with Reduced Hallucination

Timely and effective incident response is key to managing the growing frequency of cyberattacks. However, identifying the right response actions for complex systems is a major technical challenge. A promising approach to mitigate this challenge is to use the security knowledge embedded in large language models (LLMs) to assist security operators during incident handling. Recent research has demonstrated the potential of this approach, but current methods are mainly based on prompt engineering of frontier LLMs, which is costly and prone to hallucinations. We address these limitations by presenting a novel way to use an LLM for incident response planning with reduced hallucination. Our method includes three steps: fine-tuning, information retrieval, and lookahead planning. We prove that our method generates response plans with a bounded probability of hallucination and that this probability can be made arbitrarily small at the expense of increased planning time under certain assumptions. Moreover, we show that our method is lightweight and can run on commodity hardware. We evaluate our method on logs from incidents reported in the literature. The experimental results show that our method a) achieves up to 22% shorter recovery times than frontier LLMs and b) generalizes to a broad range of incident types and response actions.

Optimal Defender Strategies for CAGE-2 using Causal Modeling and Tree Search

The CAGE-2 challenge is considered a standard benchmark to compare methods for autonomous cyber defense. Current state-of-the-art methods evaluated against this benchmark are based on model-free (offline) reinforcement learning, which does not provide provably optimal defender strategies. We address this limitation and present a formal (causal) model of CAGE-2 together with a method that produces a provably optimal defender strategy, which we call Causal Partially Observable Monte-Carlo Planning (C-POMCP). It has two key properties. First, it incorporates the causal structure of the target system, i.e., the causal relationships among the system variables. This structure allows for a significant reduction of the search space of defender strategies. Second, it is an online method that updates the defender strategy at each time step via tree search. Evaluations against the CAGE-2 benchmark show that C-POMCP achieves state-of-the-art performance with respect to effectiveness and is two orders of magnitude more efficient in computing time than the closest competitor method.

Intrusion Tolerance for Networked Systems through Two-Level Feedback Control

We formulate intrusion tolerance for a system with service replicas as a two-level optimal control problem. On the local level node controllers perform intrusion recovery, and on the global level a system controller manages the replication factor. The local and global control problems can be formulated as classical problems in operations research, namely, the machine replacement problem and the inventory replenishment problem. Based on this formulation, we design TOLERANCE, a novel control architecture for intrusion-tolerant systems. We prove that the optimal control strategies on both levels have threshold structure and design efficient algorithms for computing them. We implement and evaluate TOLERANCE in an emulation environment where we run 10 types of network intrusions. The results show that TOLERANCE can improve service availability and reduce operational cost compared with state-of-the-art intrusion-tolerant systems.

Conjectural Online Learning with First-order Beliefs in Asymmetric Information Stochastic Games

Asymmetric information stochastic games (\textsc{aisg}s) arise in many complex socio-technical systems, such as cyber-physical systems and IT infrastructures. Existing computational methods for \textsc{aisg}s are primarily offline and can not adapt to equilibrium deviations. Further, current methods are limited to special classes of \textsc{aisg}s to avoid belief hierarchies. To address these limitations, we propose conjectural online learning (\textsc{col}), an online method for generic \textsc{aisg}s. \textsc{col} uses a forecaster-actor-critic (\textsc{fac}) architecture where subjective forecasts are used to conjecture the opponents' strategies within a lookahead horizon, and Bayesian learning is used to calibrate the conjectures. To adapt strategies to nonstationary environments, \textsc{col} uses online rollout with cost function approximation (actor-critic). We prove that the conjectures produced by \textsc{col} are asymptotically consistent with the information feedback in the sense of a relaxed Bayesian consistency. We also prove that the empirical strategy profile induced by \textsc{col} converges to the Berk-Nash equilibrium, a solution concept characterizing rationality under subjectivity. Experimental results from an intrusion response use case demonstrate \textsc{col}'s superiority over state-of-the-art reinforcement learning methods against nonstationary attacks.

Automated Security Response through Online Learning with Adaptive Conjectures

We study automated security response for an IT infrastructure and formulate the interaction between an attacker and a defender as a partially observed, non-stationary game. We relax the standard assumption that the game model is correctly specified and consider that each player has a probabilistic conjecture about the model, which may be misspecified in the sense that the true model has probability 0. This formulation allows us to capture uncertainty about the infrastructure and the intents of the players. To learn effective game strategies online, we design a novel method where a player iteratively adapts its conjecture using Bayesian learning and updates its strategy through rollout. We prove that the conjectures converge to best fits, and we provide a bound on the performance improvement that rollout enables with a conjectured model. To characterize the steady state of the game, we propose a variant of the Berk-Nash equilibrium. We present our method through an advanced persistent threat use case. Simulation studies based on testbed measurements show that our method produces effective security strategies that adapt to a changing environment. We also find that our method enables faster convergence than current reinforcement learning techniques.