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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

On the Sampling-Based Computation of Nash Equilibria Under Uncertainty via the Nikaido–Isoda Function

We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be L 0 -Lipschitz continuous and convex, given rival decisions with convex and closed player-specific feasibility sets. To address this problem, we consider minimizing a suitably defined value function defined using the Nikaido–Isoda function. Such an avenue does not necessitate either monotonicity properties of the concatenated gradient map or potentiality requirements on the game but does require a suitable regularity requirement under which a stationary point is a Nash equilibrium. We design and analyze a sampling-enabled projected-gradient-response method, reliant on inexact resolution of a player-level best-response subproblem. Here, by deriving suitable Lipschitzian guarantees on the value function, we derive both asymptotic guarantees for the sequence of generated iterates as well as rate and complexity guarantees for computing a stationary point by appropriate choices of the sampling rate and inexactness sequence.

Nikaido-Isoda function↗
DOE OSTI2019

Solving equilibrium problems using extended mathematical programming

We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and (quasi-) variational inequalities, and computing solutions of them from modeling languages. We define a new set of constructs with which users annotate variables and equations of the model to describe equilibrium and variational problems. Our constructs enable a natural translation of the model from one formulation to another more computationally tractable form without requiring the modeler to supply derivatives. In the context of many independent agents in the equilibrium, we facilitate expression of sophisticated structures such as shared constraints and additional constraints on their solutions. We define shared variables and demonstrate their uses for sparse reformulation, economic equilibrium problems sharing economic states, mixed pricing behavior of agents, and so on. We give some equilibrium and variational examples from the literature and describe how to formulate them using our framework. Experimental results comparing performance of various complementarity formulations for shared variables are provided. Our framework has been implemented and is available within GAMS/EMP.

Equilibrium programming↗
DOE OSTI2025

Improved Guarantees for Optimal Nash Equilibrium Seeking and Bilevel Variational Inequalities

We consider a class of hierarchical variational inequality (VI) problems that subsumes VI-constrained optimization and several other problem classes, including the optimal solution selection problem and the optimal Nash equilibrium (NE) seeking problem. Our main contribution is threefold. (i) We consider bilevel VIs with monotone and Lipschitz continuous mappings and devise a single-timescale iteratively regularized extragradient method, named IR-EG 𝚖,𝚖 . We improve the existing iteration complexity results for addressing both bilevel VI and VI-constrained convex optimization problems. (ii) Under the strong monotonicity of the outer-level mapping, we develop a method named IR-EG 𝚜,𝚖 and derive faster guarantees than those in (i). We also study the iteration complexity of this method under a constant regularization parameter. These results appear to be new for both bilevel VIs and VI-constrained optimization. (iii) To our knowledge, complexity guarantees for computing the optimal NE in nonconvex settings do not exist. Motivated by this lacuna, we consider VI-constrained nonconvex optimization problems and devise an inexactly projected gradient method, named IPR-EG, where the projection onto the unknown set of equilibria is performed using IR-EG 𝚜,𝚖 with a prescribed termination criterion and an adaptive regularization parameter. We obtain new complexity guarantees in terms of a residual map and an infeasibility metric for computing a stationary point. Here, we validate the theoretical findings using preliminary numerical experiments for computing the best and the worst NEs.

bilevel optimization↗
DOE OSTI2022

A Non-Cooperative Game-Based Distributed Beam Scheduling Framework for 5G Millimeter-Wave Cellular Networks

Here, this paper studies the problem of distributed beam scheduling for 5G millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging to different operators share the same spectrum without centralized coordination among them. Our goal is to design efficient distributed scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to the average and instantaneous power consumption constraints of the BSs. We propose a Media Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lyapunov stochastic optimization framework and non-cooperative games. In particular, we first decompose the original utility maximization problem into two sub-optimization problems for each time frame, which are a convex optimization problem and a non-convex optimization problem, respectively. By formulating the distributed scheduling problem as a non-cooperative game where each BS is a player attempting to optimize its own utility, we provide a distributed solution to the non-convex sub-optimization problem via finding the Nash Equilibrium (NE) of the game whose weights are determined optimally by the Lyapunov optimization framework. Finally, we conduct simulation under various network settings to show the effectiveness of the proposed game-based beam scheduling algorithm in comparison to that of several reference schemes.

42 ENGINEERING↗
DOE OSTI2021

Approximating Nash Equilibrium in Day-ahead Electricity Market Bidding with Multi-agent Deep Reinforcement Learning

In this paper, a day-ahead electricity market bidding problem with multiple strategic generation company (GEN-CO) bidders is studied. The problem is formulated as a Markov game model, where GENCO bidders interact with each other todevelop their optimal day-ahead bidding strategies. Considering unobservable information in the problem, a model-free and data-driven approach, known as multi-agent deep deterministic policy gradient (MADDPG), is applied for approximating the Nash equilibrium (NE) in the above Markov game. The MADDPG algorithm has the advantage of generalization due to the automatic feature extraction ability of the deep neural networks. The algorithm is tested on an IEEE 30-bus system with three competitive GENCO bidders in both an uncongested caseand a congested case. Comparisons with a truthful bidding strategy and state-of-the-art deep reinforcement learning methods including deep Q network and deep deterministic policy gradient (DDPG) demonstrate that the applied MADDPG algorithm can find a superior bidding strategy for all the market participants with increased profit gains. In addition, the comparison with a conventional model-based method shows that the MADDPG algorithm has higher computational efficiency, which is feasible for real-world applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A Non-cooperative Game-based Approach to Distributed Beam Scheduling in Millimeter-Wave Networks

We consider the distributed beam scheduling problem in mm-Wave networks where the base stations may belong to different operators and there is no centralized coordination among them. Our goal is to design distributed beam scheduling algorithms such that the network utility, which is defined as a logarithm function of the average throughput of the user equipment, can be maximized. We propose a non-cooperative game-based scheduling approach where the base stations are modeled as players that greedily maximize their own utilities. The Nash Equilibrium (NE) then provides a distributed solution to the network utility maximization problem. By employing the Lyapunov optimization, the asymptotic optimality of the proposed scheduling can be guaranteed. We prove the existence and provide sufficient conditions which guarantee the uniqueness of the NE by establishing an equivalence to the Variational Inequality (VI) problem. We also propose a parallel power adaptation algorithm which is proved to converge to the NE. Numerical results show the superiority of the proposed scheduling over several distributed baseline schemes.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

Submodular optimization problems and greedy strategies: A survey

The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How effective is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two classes of optimization problems where the objective function is submodular. The first is set submodular optimization, which is to choose a set of actions to optimize a set submodular objective function, and the second is string submodular optimization, which is to choose an ordered set of actions to optimize a string submodular function. Our emphasis here is on performance bounds for the greedy strategy in submodular optimization problems. Specifically, we review performance bounds for the greedy strategy, more general and improved bounds in terms of curvature, performance bounds for the batched greedy strategy, and performance bounds for Nash equilibria.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Automated Adversary-in-the-Loop Cyber-Physical Defense Planning

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 approximate best-response for 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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Game-Theoretic Strategies for Cyber-Physical Infrastructures Under Component Disruptions

In this work, networked infrastructures of recursively defined systems composed of discrete cyber and physical components are considered. The components of basic systems at the finest levels can be disrupted by cyber or physical means, and can be reinforced to survive at certain costs. A problem of ensuring the infrastructure performance is formulated as a game between a provider and an attacker, who probabilistically choose components to reinforce and attack, respectively. The disruptions of this infrastructure are characterized using the aggregate failure correlation function that specifies the conditional failure probability of the infrastructure given the failure of an individual system at that level. The survival probabilities of basic systems satisfy simple product-form, first-order differential equations expressed in terms of the multiplier functions. The utility functions of the provider and attacker are composed of the reward and cost terms, both expressed in terms of the component reinforcement and attack probabilities. The Nash equilibrium of this game is characterized, along with the sensitivity functions of the survival probabilities of basic systems that highlight their dependence individually on the cost-benefit terms, the correlation functions, and the multiplier functions. These results are illustrated using simplified models of a distributed cloud servers infrastructure, a 5G data network infrastructure, a high performance computing federation, and a smart energy grid infrastructure.

42 ENGINEERING↗
DOE OSTI2023

Multi-Stage Modeling With Recourse Decisions for Solving Stochastic Complementarity Problems With an Application in Energy

This paper presents a multi-stage model with recourse decisions for solving complementarity problems in a competitive electricity market under uncertainty, while also considering renewable energy technologies and battery storage utilization. The model is based on a Nash-Cournot formulation of imperfect competition among power producers. We analyze the value of variable renewable energy (VRE) and battery storage under different uncertainties, such as demand level and VRE availability. To illustrate the proposed model, we apply it to three- bus five-player model and analyze different cases varying costs, including a user-optimal perspective (with market power) and a system-optimal perspective (with central planning). We also consider the potential for congestion in the system by restricting the transmission capacity between a single interface that connects two buses. Our findings show that increasing the battery storage capacity results in a decrease in the need for perfect information about future uncertainties. Additionally, as the model allows for more uncertainty, it becomes more apparent that the stochastic mixed complementarity problem (MCP) has an advantage over a deterministic equivalent. We propose the use of the Value of the Stochastic Equilibrium Solution (VSES) as a quality metric to compare the stochastic MCP with its deterministic equivalent. Overall, expanding battery storage capacity can lower the maximum, mean, and variance values of delivered prices, but there are diminishing returns to this approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗