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  1. Security of cyber-physical systems (CPS) continues to pose new challenges due to the tight integration and operational complexity of the cyber and physical components. To address these challenges, this article presents a domain-aware, optimization-based approach to determine an effective defense strategy for CPS in an automated fashion—by emulating a strategic adversary in the loop that exploits system vulnerabilities, interconnection of the CPS, and the dynamics of the physical components. Our approach builds on an adversarial decision-making model based on a Markov Decision Process (MDP) that determines the optimal cyber (discrete) and physical (continuous) attack actions over a CPS attack graph. The defense planning problem is modeled as a non-zero-sum game between the adversary and defender. We use a model-free reinforcement learning method to solve the adversary’s problem as a function of the defense strategy. We then employ Bayesian optimization (BO) to find an approximatebest-responsefor the defender to harden the network against the resulting adversary policy. This process is iterated multiple times to improve the strategy for both players. We demonstrate the effectiveness of our approach on a ransomware-inspired graph with a smart building system as the physical process. Numerical studies show that our method converges to a Nash equilibrium for various defender-specific costs of network hardening.

     
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    Free, publicly-accessible full text available July 31, 2024
  2. Free, publicly-accessible full text available May 31, 2024
  3. Fang, F. (Ed.)
  4. Fang, F. (Ed.)
  5. We consider a prototypical path planning problem on a graph with uncertain cost of mobility on its edges. At a given node, the planning agent can access the true cost for edges to its neighbors and uses a noisy simulator to estimate the cost-to-go from the neighboring nodes. The objective of the planning agent is to select a neighboring node such that, with high probability, the cost-to-go is minimized for the worst possible realization of uncertain parameters in the simulator. By modeling the cost-to-go as a Gaussian process (GP) for every realization of the uncertain parameters, we apply a scenario approach in which we draw fixed independent samples of the uncertain parameter. We present a scenario-based iterative algorithm using the upper confidence bound (UCB) of the fixed independent scenarios to compute the choice of the neighbor to go to. We characterize the performance of the proposed algorithm in terms of a novel notion of regret defined with respect to an additional draw of the uncertain parameter, termed as scenario regret under re-draw. In particular, we characterize a high probability upper bound on the regret under re-draw for any finite number of iterations of the algorithm, and show that this upper bound tends to zero asymptotically with the number of iterations. We supplement our analysis with numerical results. 
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  6. null (Ed.)