Kim Hammar

Kim Hammar, Yuchao Li, Tansu Alpcan et al.

Evolving security vulnerabilities and shifting operational conditions require frequent updates to network security policies. These updates include adjustments to incident response procedures and modifications to access controls, among others. Reinforcement learning methods have been proposed for automating such policy adaptations, but most methods in the research literature lack performance guarantees and adapt slowly to changes. In this paper, we address these limitations and present a method for computing security policies that is scalable, offers theoretical guarantees, and adapts quickly to changes. The method uses a model or simulator of the system, which is updated when changes occur, and combines three components: belief estimation through particle filtering, offline policy computation through feature-based aggregation, and online policy adaptation through rollout. In particular, feature-based aggregation enables scalable offline optimization of a policy, while rollout adapts the policy online to changes in the system model without repeating the offline optimization. We analyze the approximation error of the aggregation and show that the rollout efficiently adapts policies to changes under certain conditions. Simulations and testbed results demonstrate that our method outperforms state-of-the-art methods on several benchmarks, including CAGE-2.

Kim Hammar, Rolf Stadler

We study automated intrusion response and formulate the interaction between an attacker and a defender as an optimal stopping game where attack and defense strategies evolve through reinforcement learning and self-play. The game-theoretic modeling enables us to find defender strategies that are effective against a dynamic attacker, i.e. an attacker that adapts its strategy in response to the defender strategy. Further, the optimal stopping formulation allows us to prove that optimal strategies have threshold properties. To obtain near-optimal defender strategies, we develop Threshold Fictitious Self-Play (T-FP), a fictitious self-play algorithm that learns Nash equilibria through stochastic approximation. We show that T-FP outperforms a state-of-the-art algorithm for our use case. The experimental part of this investigation includes two systems: a simulation system where defender strategies are incrementally learned and an emulation system where statistics are collected that drive simulation runs and where learned strategies are evaluated. We argue that this approach can produce effective defender strategies for a practical IT infrastructure.

Kim Hammar, Rolf Stadler

We study automated intrusion prevention using reinforcement learning. Following a novel approach, we formulate the interaction between an attacker and a defender as an optimal stopping game and let attack and defense strategies evolve through reinforcement learning and self-play. The game-theoretic perspective allows us to find defender strategies that are effective against dynamic attackers. The optimal stopping formulation gives us insight into the structure of optimal strategies, which we show to have threshold properties. To obtain the optimal defender strategies, we introduce T-FP, a fictitious self-play algorithm that learns Nash equilibria through stochastic approximation. We show that T-FP outperforms a state-of-the-art algorithm for our use case. Our overall method for learning and evaluating strategies includes two systems: a simulation system where defender strategies are incrementally learned and an emulation system where statistics are produced that drive simulation runs and where learned strategies are evaluated. We conclude that this approach can produce effective defender strategies for a practical IT infrastructure.

Kim Hammar, Rolf Stadler

We present a system for interactive examination of learned security policies. It allows a user to traverse episodes of Markov decision processes in a controlled manner and to track the actions triggered by security policies. Similar to a software debugger, a user can continue or or halt an episode at any time step and inspect parameters and probability distributions of interest. The system enables insight into the structure of a given policy and in the behavior of a policy in edge cases. We demonstrate the system with a network intrusion use case. We examine the evolution of an IT infrastructure's state and the actions prescribed by security policies while an attack occurs. The policies for the demonstration have been obtained through a reinforcement learning approach that includes a simulation system where policies are incrementally learned and an emulation system that produces statistics that drive the simulation runs.

Kim Hammar, Tansu Alpcan, Emil Lupu

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.

Kim Hammar, Neil Dhir, Rolf Stadler

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.

Kim Hammar, Rolf Stadler

We study automated intrusion response for an IT infrastructure and formulate the interaction between an attacker and a defender as a partially observed stochastic game. To solve the game we follow an approach where attack and defense strategies co-evolve through reinforcement learning and self-play toward an equilibrium. Solutions proposed in previous work prove the feasibility of this approach for small infrastructures but do not scale to realistic scenarios due to the exponential growth in computational complexity with the infrastructure size. We address this problem by introducing a method that recursively decomposes the game into subgames which can be solved in parallel. Applying optimal stopping theory we show that the best response strategies in these subgames exhibit threshold structures, which allows us to compute them efficiently. To solve the decomposed game we introduce an algorithm called Decompositional Fictitious Self-Play (DFSP), which learns Nash equilibria through stochastic approximation. We evaluate the learned strategies in an emulation environment where real intrusions and response actions can be executed. The results show that the learned strategies approximate an equilibrium and that DFSP significantly outperforms a state-of-the-art algorithm for a realistic infrastructure configuration.

Kim Hammar, Neil Dhir

We consider the problem of optimising an expensive-to-evaluate grey-box objective function, within a finite budget, where known side-information exists in the form of the causal structure between the design variables. Standard black-box optimisation ignores the causal structure, often making it inefficient and expensive. The few existing methods that consider the causal structure are myopic and do not fully accommodate the observation-intervention trade-off that emerges when estimating causal effects. In this paper, we show that the observation-intervention trade-off can be formulated as a non-myopic optimal stopping problem which permits an efficient solution. We give theoretical results detailing the structure of the optimal stopping times and demonstrate the generality of our approach by showing that it can be integrated with existing causal Bayesian optimisation algorithms. Experimental results show that our formulation can enhance existing algorithms on real and synthetic benchmarks.

Kim Hammar

Reinforcement learning is a promising approach to autonomous and adaptive security management in networked systems. However, current reinforcement learning solutions for security management are mostly limited to simulation environments and it is unclear how they generalize to operational systems. In this paper, we address this limitation by presenting CSLE: a reinforcement learning platform for autonomous security management that enables experimentation under realistic conditions. Conceptually, CSLE encompasses two systems. First, it includes an emulation system that replicates key components of the target system in a virtualized environment. We use this system to gather measurements and logs, based on which we identify a system model, such as a Markov decision process. Second, it includes a simulation system where security strategies are efficiently learned through simulations of the system model. The learned strategies are then evaluated and refined in the emulation system to close the gap between theoretical and operational performance. We demonstrate CSLE through four use cases: flow control, replication control, segmentation control, and recovery control. Through these use cases, we show that CSLE enables near-optimal security management in an environment that approximates an operational system.

Yiran Gao, Kim Hammar, Tao Li

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.

Tao Li, Kim Hammar, Rolf Stadler et al.

Asymmetric information stochastic games (AISGs) arise in many complex socio-technical systems, such as cyber-physical systems and IT infrastructures. Existing computational methods for AISGs are primarily offline and can not adapt to equilibrium deviations. Further, current methods are limited to particular information structures to avoid belief hierarchies. Considering these limitations, we propose conjectural online learning (COL), an online learning method under generic information structures in AISGs. COL uses a forecaster-actor-critic (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 based on information feedback, COL uses online rollout with cost function approximation (actor-critic). We prove that the conjectures produced by 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 COL converges to the Berk-Nash equilibrium, a solution concept characterizing rationality under subjectivity. Experimental results from an intrusion response use case demonstrate COL's {faster convergence} over state-of-the-art reinforcement learning methods against nonstationary attacks.

Kim Hammar, Tao Li, Rolf Stadler et al.

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 and misconception about the infrastructure and the intents of the players. To learn effective game strategies online, we design Conjectural Online Learning (COL), 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 COL through an advanced persistent threat use case. Testbed evaluations show that COL produces effective security strategies that adapt to a changing environment. We also find that COL enables faster convergence than current reinforcement learning techniques.

Kim Hammar, Rolf Stadler

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.

Kim Hammar, Tansu Alpcan, Emil C. Lupu

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.

Kim Hammar, Tao Li

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.

Kim Hammar, Rolf Stadler

Identifying a causal model of an IT system is fundamental to many branches of systems engineering and operation. Such a model can be used to predict the effects of control actions, optimize operations, diagnose failures, detect intrusions, etc., which is central to achieving the longstanding goal of automating network and system management tasks. Traditionally, causal models have been designed and maintained by domain experts. This, however, proves increasingly challenging with the growing complexity and dynamism of modern IT systems. In this paper, we present the first principled method for online, data-driven identification of an IT system in the form of a causal model. The method, which we call active causal learning, estimates causal functions that capture the dependencies among system variables in an iterative fashion using Gaussian process regression based on system measurements, which are collected through a rollout-based intervention policy. We prove that this method is optimal in the Bayesian sense and that it produces effective interventions. Experimental validation on a testbed shows that our method enables accurate identification of a causal system model while inducing low interference with system operations.

Kim Hammar, Rolf Stadler

We study automated intrusion prevention using reinforcement learning. Following a novel approach, we formulate the problem of intrusion prevention as an (optimal) multiple stopping problem. This formulation gives us insight into the structure of optimal policies, which we show to have threshold properties. For most practical cases, it is not feasible to obtain an optimal defender policy using dynamic programming. We therefore develop a reinforcement learning approach to approximate an optimal threshold policy. We introduce T-SPSA, an efficient reinforcement learning algorithm that learns threshold policies through stochastic approximation. We show that T-SPSA outperforms state-of-the-art algorithms for our use case. Our overall method for learning and validating policies includes two systems: a simulation system where defender policies are incrementally learned and an emulation system where statistics are produced that drive simulation runs and where learned policies are evaluated. We show that this approach can produce effective defender policies for a practical IT infrastructure.

Kim Hammar, Rolf Stadler

We study automated intrusion prevention using reinforcement learning. In a novel approach, we formulate the problem of intrusion prevention as an optimal stopping problem. This formulation allows us insight into the structure of the optimal policies, which turn out to be threshold based. Since the computation of the optimal defender policy using dynamic programming is not feasible for practical cases, we approximate the optimal policy through reinforcement learning in a simulation environment. To define the dynamics of the simulation, we emulate the target infrastructure and collect measurements. Our evaluations show that the learned policies are close to optimal and that they indeed can be expressed using thresholds.

Kim Hammar, Rolf Stadler

We present a method to automatically find security strategies for the use case of intrusion prevention. Following this method, we model the interaction between an attacker and a defender as a Markov game and let attack and defense strategies evolve through reinforcement learning and self-play without human intervention. Using a simple infrastructure configuration, we demonstrate that effective security strategies can emerge from self-play. This shows that self-play, which has been applied in other domains with great success, can be effective in the context of network security. Inspection of the converged policies show that the emerged policies reflect common-sense knowledge and are similar to strategies of humans. Moreover, we address known challenges of reinforcement learning in this domain and present an approach that uses function approximation, an opponent pool, and an autoregressive policy representation. Through evaluations we show that our method is superior to two baseline methods but that policy convergence in self-play remains a challenge.

Kim Hammar, Shatha Jaradat, Nima Dokoohaki et al.

With the advent of social media, our online feeds increasingly consist of short, informal, and unstructured text. This textual data can be analyzed for the purpose of improving user recommendations and detecting trends. Instagram is one of the largest social media platforms, containing both text and images. However, most of the prior research on text processing in social media is focused on analyzing Twitter data, and little attention has been paid to text mining of Instagram data. Moreover, many text mining methods rely on annotated training data, which in practice is both difficult and expensive to obtain. In this paper, we present methods for unsupervised mining of fashion attributes from Instagram text, which can enable a new kind of user recommendation in the fashion domain. In this context, we analyze a corpora of Instagram posts from the fashion domain, introduce a system for extracting fashion attributes from Instagram, and train a deep clothing classifier with weak supervision to classify Instagram posts based on the associated text. With our experiments, we confirm that word embeddings are a useful asset for information extraction. Experimental results show that information extraction using word embeddings outperforms a baseline that uses Levenshtein distance. The results also show the benefit of combining weak supervision signals using generative models instead of majority voting. Using weak supervision and generative modeling, an F1 score of 0.61 is achieved on the task of classifying the image contents of Instagram posts based solely on the associated text, which is on level with human performance. Finally, our empirical study provides one of the few available studies on Instagram text and shows that the text is noisy, that the text distribution exhibits the long-tail phenomenon, and that comment sections on Instagram are multi-lingual.