Reinforcement Learning for Industrial Control Network Cyber Security Orchestration

Defending computer networks from cyber attack requires coordinating actions across multiple nodes based on imperfect indicators of compromise while minimizing disruptions to network operations. Advanced attacks can progress with few observable signals over several months before execution. The resulting sequential decision problem has large observation and action spaces and a long time-horizon, making it difficult to solve with existing methods. In this work, we present techniques to scale deep reinforcement learning to solve the cyber security orchestration problem for large industrial control networks. We propose a novel attention-based neural architecture with size complexity that is invariant to the size of the network under protection. A pre-training curriculum is presented to overcome early exploration difficulty. Experiments show in that the proposed approaches greatly improve both the learning sample complexity and converged policy performance over baseline methods in simulation.

ZoPE: A Fast Optimizer for ReLU Networks with Low-Dimensional Inputs

Deep neural networks often lack the safety and robustness guarantees needed to be deployed in safety critical systems. Formal verification techniques can be used to prove input-output safety properties of networks, but when properties are difficult to specify, we rely on the solution to various optimization problems. In this work, we present an algorithm called ZoPE that solves optimization problems over the output of feedforward ReLU networks with low-dimensional inputs. The algorithm eagerly splits the input space, bounding the objective using zonotope propagation at each step, and improves computational efficiency compared to existing mixed integer programming approaches. We demonstrate how to formulate and solve three types of optimization problems: (i) minimization of any convex function over the output space, (ii) minimization of a convex function over the output of two networks in series with an adversarial perturbation in the layer between them, and (iii) maximization of the difference in output between two networks. Using ZoPE, we observe a $25\times$ speedup on property 1 of the ACAS Xu neural network verification benchmark and an $85\times$ speedup on a set of linear optimization problems. We demonstrate the versatility of the optimizer in analyzing networks by projecting onto the range of a generative adversarial network and visualizing the differences between a compressed and uncompressed network.

Measurable Monte Carlo Search Error Bounds

Monte Carlo planners can often return sub-optimal actions, even if they are guaranteed to converge in the limit of infinite samples. Known asymptotic regret bounds do not provide any way to measure confidence of a recommended action at the conclusion of search. In this work, we prove bounds on the sub-optimality of Monte Carlo estimates for non-stationary bandits and Markov decision processes. These bounds can be directly computed at the conclusion of the search and do not require knowledge of the true action-value. The presented bound holds for general Monte Carlo solvers meeting mild convergence conditions. We empirically test the tightness of the bounds through experiments on a multi-armed bandit and a discrete Markov decision process for both a simple solver and Monte Carlo tree search.

Verification of Image-based Neural Network Controllers Using Generative Models

Neural networks are often used to process information from image-based sensors to produce control actions. While they are effective for this task, the complex nature of neural networks makes their output difficult to verify and predict, limiting their use in safety-critical systems. For this reason, recent work has focused on combining techniques in formal methods and reachability analysis to obtain guarantees on the closed-loop performance of neural network controllers. However, these techniques do not scale to the high-dimensional and complicated input space of image-based neural network controllers. In this work, we propose a method to address these challenges by training a generative adversarial network (GAN) to map states to plausible input images. By concatenating the generator network with the control network, we obtain a network with a low-dimensional input space. This insight allows us to use existing closed-loop verification tools to obtain formal guarantees on the performance of image-based controllers. We apply our approach to provide safety guarantees for an image-based neural network controller for an autonomous aircraft taxi problem. We guarantee that the controller will keep the aircraft on the runway and guide the aircraft towards the center of the runway. The guarantees we provide are with respect to the set of input images modeled by our generator network, so we provide a recall metric to evaluate how well the generator captures the space of plausible images.

Training Structured Mechanical Models by Minimizing Discrete Euler-Lagrange Residual

Model-based paradigms for decision-making and control are becoming ubiquitous in robotics. They rely on the ability to efficiently learn a model of the system from data. Structured Mechanical Models (SMMs) are a data-efficient black-box parameterization of mechanical systems, typically fit to data by minimizing the error between predicted and observed accelerations or next states. In this work, we propose a methodology for fitting SMMs to data by minimizing the discrete Euler-Lagrange residual. To study our methodology, we fit models to joint-angle time-series from undamped and damped double-pendulums, studying the quality of learned models fit to data with and without observation noise. Experiments show that our methodology learns models that are better in accuracy to those of the conventional schemes for fitting SMMs. We identify use cases in which our method is a more appropriate methodology. Source code for reproducing the experiments is available at https://github.com/sisl/delsmm.

Preference-based Learning of Reward Function Features

Preference-based learning of reward functions, where the reward function is learned using comparison data, has been well studied for complex robotic tasks such as autonomous driving. Existing algorithms have focused on learning reward functions that are linear in a set of trajectory features. The features are typically hand-coded, and preference-based learning is used to determine a particular user's relative weighting for each feature. Designing a representative set of features to encode reward is challenging and can result in inaccurate models that fail to model the users' preferences or perform the task properly. In this paper, we present a method to learn both the relative weighting among features as well as additional features that help encode a user's reward function. The additional features are modeled as a neural network that is trained on the data from pairwise comparison queries. We apply our methods to a driving scenario used in previous work and compare the predictive power of our method to that of only hand-coded features. We perform additional analysis to interpret the learned features and examine the optimal trajectories. Our results show that adding an additional learned feature to the reward model enhances both its predictive power and expressiveness, producing unique results for each user.

Generating Probabilistic Safety Guarantees for Neural Network Controllers

Neural networks serve as effective controllers in a variety of complex settings due to their ability to represent expressive policies. The complex nature of neural networks, however, makes their output difficult to verify and predict, which limits their use in safety-critical applications. While simulations provide insight into the performance of neural network controllers, they are not enough to guarantee that the controller will perform safely in all scenarios. To address this problem, recent work has focused on formal methods to verify properties of neural network outputs. For neural network controllers, we can use a dynamics model to determine the output properties that must hold for the controller to operate safely. In this work, we develop a method to use the results from neural network verification tools to provide probabilistic safety guarantees on a neural network controller. We develop an adaptive verification approach to efficiently generate an overapproximation of the neural network policy. Next, we modify the traditional formulation of Markov decision process (MDP) model checking to provide guarantees on the overapproximated policy given a stochastic dynamics model. Finally, we incorporate techniques in state abstraction to reduce overapproximation error during the model checking process. We show that our method is able to generate meaningful probabilistic safety guarantees for aircraft collision avoidance neural networks that are loosely inspired by Airborne Collision Avoidance System X (ACAS X), a family of collision avoidance systems that formulates the problem as a partially observable Markov decision process (POMDP).

Learning Emergent Discrete Message Communication for Cooperative Reinforcement Learning

Communication is a important factor that enables agents work cooperatively in multi-agent reinforcement learning (MARL). Most previous work uses continuous message communication whose high representational capacity comes at the expense of interpretability. Allowing agents to learn their own discrete message communication protocol emerged from a variety of domains can increase the interpretability for human designers and other agents.This paper proposes a method to generate discrete messages analogous to human languages, and achieve communication by a broadcast-and-listen mechanism based on self-attention. We show that discrete message communication has performance comparable to continuous message communication but with much a much smaller vocabulary size.Furthermore, we propose an approach that allows humans to interactively send discrete messages to agents.

Scalable Anytime Planning for Multi-Agent MDPs

We present a scalable tree search planning algorithm for large multi-agent sequential decision problems that require dynamic collaboration. Teams of agents need to coordinate decisions in many domains, but naive approaches fail due to the exponential growth of the joint action space with the number of agents. We circumvent this complexity through an anytime approach that allows us to trade computation for approximation quality and also dynamically coordinate actions. Our algorithm comprises three elements: online planning with Monte Carlo Tree Search (MCTS), factored representations of local agent interactions with coordination graphs, and the iterative Max-Plus method for joint action selection. We evaluate our approach on the benchmark SysAdmin domain with static coordination graphs and achieve comparable performance with much lower computation cost than our MCTS baselines. We also introduce a multi-drone delivery domain with dynamic, i.e., state-dependent coordination graphs, and demonstrate how our approach scales to large problems on this domain that are intractable for other MCTS methods. We provide an open-source implementation of our algorithm at https://github.com/JuliaPOMDP/FactoredValueMCTS.jl.

Transfer Learning for Efficient Iterative Safety Validation

Safety validation is important during the development of safety-critical autonomous systems but can require significant computational effort. Existing algorithms often start from scratch each time the system under test changes. We apply transfer learning to improve the efficiency of reinforcement learning based safety validation algorithms when applied to related systems. Knowledge from previous safety validation tasks is encoded through the action value function and transferred to future tasks with a learned set of attention weights. Including a learned state and action value transformation for each source task can improve performance even when systems have substantially different failure modes. We conduct experiments on safety validation tasks in gridworld and autonomous driving scenarios. We show that transfer learning can improve the initial and final performance of validation algorithms and reduce the number of training steps.