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28 records · Page 2

Adaptive Cybersecurity for Distributed Energy Resources (AdCyDER): Online Reinforcement Learning with Stackelberg-Optimized Defenses — Pipeline Architecture, Evaluation Methodology, and Findings from a Synthetic-Data Evaluation

This report documents the design and evaluation of an integrated online-learning pipeline developed within the AdCyDER project for Distributed Energy Resource (DER) cybersecurity. The pipeline couples a Reinforcement Learning (RL) attack classifier — which produces an attack-type probability distribution — with a Stackelberg game-theoretic (GT) defense selector that consumes those distributions alongside SME-encoded priors over (defense, attack) effectiveness pairings and perdefense costs to choose grid-health-preserving defenses. The objective is not attack classification per se but production of distributions that drive effective defense selection through the Stackelberg layer, learned from delayed grid-health feedback rather than labeled attack data. AdCyDER as a whole is broader than the work presented here; this report covers the specific RL/GT loop integration and its evaluation. We present the integrated pipeline (SCADA telemetry with Fronius inverter physics, Suricata IDS, time-windowed aggregation, per-facility LSTM classifier, Stackelberg optimizer, OpenC2 actuators), an experimental campaign of 28 eight-hour iterations across three baseline modes, and a pipeline-ordered diagnostic protocol. The protocol identifies two distinct failure modes within the loop: paired supervised ceilings on the same features establish that the deployed online RL classifier (macro F1 ≈ 0.07) sits at least 4.7× below a same-architecture supervised LSTM (≈ 0.34) and 10–11× below a linear feature-signal ceiling (≈ 0.70–0.79 depending on per-facility isolation), localizing the dominant failure to the training procedure; and the reward signal driving online updates carries weak directional coupling with classifier correctness in the methodology-expected direction (multi-lens convergent: top-decile P(true) records produce more frequent state changes and slightly larger improvements, top-vs-bot Cohen’s 𝑑 ≈ −0.19), but at effect magnitudes too small to drive gradient-based learning at the campaign sample size. The original learning hypothesis is not supported by the data. The primary contributions are the diagnostic methodology — proposed as a transferable falsification protocol for online RL/GT defense pipelines learning from delayed environmental reward — and the open, reproducible experimental infrastructure. We outline reward reformulation as the highest-priority aspirational next step given the underpowered-but-aligned Q6 reading, with hardware-in-the-loop evaluation as the broadest scope-expansion option.

Blakely, Benjamin [Argonne National Laboratory (AN↗

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗

Power system resilience through defender-attacker-defender models with uncertainty: an overview

Protecting and fortifying a power system to make it resilient is an important and hard problem to solve. The interaction between defenders and attackers, the availability of information and the complexity of power system require carefully selecting models and presenting the underlying assumptions. Trilevel defender-attacker-defender models have been developed to investigate the resilience of power systems. In this paper, we review trilevel models in power system application, with the aim of demonstrating the accessibility and applicability of these complex optimization formulations and discussing the underlying assumptions from these models. In particular, we highlight modeling choices, algorithmic details, and how operational and information uncertainty affects resilience versus the traditional complete-knowledge-based optimal solutions. We also describe other similar relevant models which lack such uncertainty and discuss insights on how to address operational, attacker, and defender related uncertainties in future research efforts.

multi-level optimization, defender-attacker-defend↗

Buyers Collusion in Incentivized Forwarding Networks: A Multi-Agent Reinforcement Learning Study

We present the issue of monetarily incentivized forwarding in a multi-hop mesh network architecture from an economic perspective. It is anticipated that credit-incentivized forwarding and relaying will be a simple method of exchanging transmission power and spectrum for connectivity. However, gateways and forwarding nodes, like any other free market, may create an oligopolistic market for the users they serve. In this study, a coalition scheme between buyers aims to address price control by gateways or nodes closer to gateways. In a Stackelberg competition game, buyer agents (users) and sellers (gateways) make decisions using reinforcement learning (RL), with decentralized Deep Q-Networks to buy and sell forwarding resources. We allow communication links between the buyers with a limited messaging space, without defining a collusion mechanism. The idea is to demonstrate that through messaging, and RL tacit collusion can emerge between agents in a decentralized setup. The multi-agent reinforcement learning (MARL) system is presented and analyzed from a machine-learning perspective. Moreover, MARL dynamics are discussed via mean field analysis to better understand divergence causes and make implementation recommendations for such systems. Finally, the simulation results show the results of coordination among the users.

42 ENGINEERING↗

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Preprint

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

distribution system operator↗

Game Theoretic Approach to Post-Docked Satellite Control

This paper studies the interaction between two satellites after docking. In order to maintain the docked state with uncertainty in the motion of the target vehicle, a game theoretic controller with Stackelberg strategy to minimize the interaction between the satellites is considered. The small perturbation approximation leads to LQ differential game scheme, which is validated to address the docking interactions between a service vehicle and a target vehicle. The open-loop solution are compared with Nash strategy, and it is shown that less control efforts are obtained with Stackelberg strategy.

Hiramatsu, Takashi↗

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗

On a cost functional for H2/H(infinity) minimization

A cost functional is proposed and investigated which is motivated by minimizing the energy in a structure using only collocated feedback. Defined for an H(infinity)-norm bounded system, this cost functional also overbounds the H2 cost. Some properties of this cost functional are given, and preliminary results on the procedure for minimizing it are presented. The frequency domain cost functional is shown to have a time domain representation in terms of a Stackelberg non-zero sum differential game.

Macmartin, Douglas G.↗

A comparison study on trading behavior and profit distribution in local energy transaction games

With the increasing integration of distributed energy resources, localized peer-to-peer energy transactions are receiving more attention since they could absorb more distributed renewables locally and stabilize the power grid. To better study the trading behavior and provide guidance for a viable local market design, different game-theoretical frameworks including cooperative and non-cooperative games are established and compared here. For the cooperative grand coalition, the maximum social welfare is guaranteed, the Shapley value and bargaining based approaches are implemented for further profit redistribution. It is shown that the asymmetrical bargaining power can be critical in the final payment clearing and it is equivalent to the Shapley value allocation if prosumers bargain based on their marginal contributions. Non-cooperative trading is formulated by using a Stackelberg bilevel model in which the upper level has the privilege in internal price setting. However, system optimum is not obtained due to competition, and the selfish leader could take away 89% of the collective benefit by price-gap based arbitraging. Aiming for a long-lasting trading market, a virtual benevolent leader and a uniform price structure in which purchase price equals selling price are tested. Experimental results indicate that maximum social welfare and a fairer profit allocation can be achieved with a uniform price structure, regardless of the selfish or benevolent attitude.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗