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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Finding Bounded Rational Equilibria: Iterative Focusing - Part 1

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights from the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Wolpert, David H.↗
NASA NTRS2004

Finding Bounded Rational Equilibria: Alternative Lagrangians and Uncountable Move Spaces - Part 2

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights &om the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Wolpert, David H.↗
DOE OSTI2022

Hierarchical Model-Free Transactive Control of Building Loads to Support Grid Services

Residential buildings consume 4.4 quads of electricity annually, approximately 37% of the total electricity consumption in the United States. This represents a vast resource that can be used for demand management and other ancillary services. This project aims to develop a robust, scalable hierarchical transactional control mechanism incorporating elements of model-free control (MFC) and game theory to harness buildings to provide ancillary services to the grid. This approach is being taken to address the challenges of incorporating traditional transactional control schemes into existing buildings. The challenges include small individual building sizes requiring aggregation of many buildings, unpredictable energy usage that makes model identification difficult, and satisfying the sensitive occupant comfort constraints. In the proposed approach, by separating the control mechanism into two layers above and below the load aggregator, MFC can be used below the aggregator to modulate flexible building loads in response to pricing signals with guaranteed performance. This allows the burden of identifying an accurate model of the system to be shifted to the above-aggregator layer, where fluctuations in individual building usage have less impact on predicted building system behavior. Game theory concepts can then be used to determine pricing curves and control signals among regional aggregators. Managing this control in a game-theoretic approach will allow us to build in financial incentives that increase customer engagement. Additionally, the usage of MFC necessitates less burdensome computational and communication requirements, thus, it is easily deployable on small, embedded devices. In a broader sense, developing a strategy capable of effectively incorporating residential and small commercial buildings will allow greater throughput of existing and emerging grid services in addition to future transactive energy grid management methods. Using MFC within a hierarchical control architecture will allow the shifting of existing forecasting challenges to an aggregate level, where dynamics are slower and more predictable. This will enable a smooth interface between the grid services requests of utilities and the reliable control required by participating buildings. MFC, which supports distributed control architecture, permits a scalable solution that can be deployed to neighborhood-size systems as well as individual buildings. This project focuses on three objectives: (1) developing the mathematical framework, algorithm toolkit, and software toolset of the two-layer transactive control testbed; (2) developing a scalable solution for application over many residential and small-size commercial buildings with sparse distributed communication; and (3) field testing and implementation on hardware of the control strategies developed in the previous two objectives. The research and development activities are focused and designed to be impactful within the relevant 2025 targets timeframe. An open-source control framework for exploiting variability and dispatchability of building loads will be delivered as the outcome of the project. This capability enables greater participation of loads in electricity markets and ancillary services that are both useful for the utility and financially beneficial for building owners.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

From Modular ADMS to Plug-and-Play Ops: Distribution Grid Operations with Platform-Level Orchestration to Enable Ambitious App Hosting

The core function of the distribution grid is to provide electricity to consumers affordably, reliably, and securely. In pursuing these core objectives, distribution utilities are accountable to customers, regulators, and in some cases, shareholders. Other third parties such as aggregators and microgrids can also have a stake in the smooth operation of the grid. Each of these stakeholders has economic, business, and/or governance objectives that inform their expectations of the distribution grid. This multi-objective, multi-stakeholder environment creates tension that must be reconciled to successfully design and operate the distribution grid. Innovative companies are competing to bring high-tech solutions to electric utilities and their customers that address each of these objectives. Many developers of advanced distribution management systems (ADMS) and distributed energy resource management systems (DERMS) have adopted a modular architecture that allows grid operators to select functions and features according to their individual system needs. A modular platform also allows the solution provider to develop and integrate specific new product modules; however, the need to pursue multiple objectives with a fixed set of controllable devices makes integration expensive whether it is done at the product development stage or the deployment stage. This cost creates a significant barrier to adoption and can lengthen the product to market time of new solutions. To fundamentally address the complexity of system integration for distribution grid operations, the U.S. Department of Energy Office of Electricity has funded the GridAPPS-D project at PNNL, which streamlines integration by contributing to standards development, defining system architecture, applying advanced mathematics, and developing open-source software to demonstrate the concept of an open data-integration platform for distribution operations. The open data-integration platform concept enables system operators and solution providers to deploy ambitious, best-of-breed applications (or apps) without continually reengineering for integration. Ambitious apps developed by different solution providers will inevitably attempt to achieve different control objectives with the same set of controllable devices. If the open platform itself can resolve these conflicts in a way that achieves the best available outcomes for all apps, doesn’t restrict the ambitious design of apps, and ensures safe and secure operations, apps will be able to plug-and-play with the platform at the same time as other ambitious apps. In this paper, we describe a framework called App Deconfliction that empowers a platform to assign setpoints to controllable devices based on the values preferred by different apps (and even external stakeholder entities like customers or aggregators). The App Deconfliction framework is compatible with several methods for determining setpoint values. We present two methods based on game theory that provide a subtle built-in incentive structure for developers to adapt their apps to the fact that they will be operating in a moderated multi-app environment and to favor device setpoints that have the most effect on their objectives over those that have the least effect. Our simulation-based demonstrations have shown that game-theory-based deconfliction can lead to a 7% improvement in control space utilization compared to design-based methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Mutual Detectability: A Targeted SETI Strategy That Avoids the SETI Paradox

As our ability to undertake searches for extraterrestrial intelligence (SETI) grows, so does interest in the controversial endeavor of messaging extraterrestrial intelligence (METI). METI proponents point to the SETI Paradox—if all civilizations refrain from METI then SETI is futile. I introduce mutual detectability as a game-theoretic strategy to increase the success potential of targeted SETI. Mutual detectability comprises four laws that establish how SETI participants can engage each other based on mutual evidence of mutual existence. I argue that the party whom both SETI participants can judge to have better quality evidence, or common denominator information (CDI), has an onus to transmit to avoid the SETI Paradox. Transiting exoplanets within the Earth Transit Zone form a target subset that satisfies mutual detectability requirements. I identify the intrinsic time-integrated transit signal strength, which for Earth is 10{sup 3} L{sub ⊙} ppm hours yr{sup −1}, as suitable CDI. Civilizations on habitable-zone planets of radius R{sub p}/R{sub ⊕}≲(L{sub ∗}/L{sub ⊙}){sup −1/7} have superior CDI on us, and so under the mutual detectability framework have game-theory incentive (onus) to transmit. While the onus to transmit falls on us for habitable planets around L{sub *} > L{sub ⊙} stars, considerations of relative stellar frequency, main-sequence lifetime and planet occurrence rates mean that such systems are likely to be in a small minority. Surveys of the Earth Transit Zone for Earth-analog transiting planets around subsolar luminosity hosts would facilitate targeted SETI programs for civilizations who have game-theory incentive to transmit signals to us. A choice to remain silent, by not engaging in METI toward such systems, does not in this case fuel concerns of a SETI Paradox.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Hypergames and Cyber-Physical Security for Control Systems

The identification of the Stuxnet worm in 2010 provided a highly publicized example of a cyber attack that physically damaged an industrial control system. This raised public awareness about the possibility of similar attacks against other industrial targets—including critical infrastructure. Here, we use hypergames to analyze how strategic perturbations of sensor readings and calibrated parameters can be used to manipulate a system that employs optimal control. Hypergames form an extension of game theory that enables us to model strategic interactions where the players may have significantly different perceptions of the game(s) they are playing. Past work with hypergames has focused on relatively simple interactions consisting of a small set of discrete choices for each player. Here, we apply single-stage hypergames to larger systems with continuous variables. We find that manipulating constraints can be a more effective attacker strategy than manipulating objective function parameters. Moreover, the attacker need not change the underlying system to carry out a successful attack—it may be sufficient to deceive the defender controlling the system. It is possible to scale our approach up to even larger systems, but this will depend on the characteristics of the system in question, and we identify several characteristics that will make those systems amenable to hypergame analysis.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Distributed Constrained Optimization with Semicoordinate Transformations

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Macready, William↗
NASA NTRS1975

A state-of-the-art review of transportation systems evaluation techniques relevant to air transportation, volume 1

Mathematical and philosophical approaches are presented for evaluation and implementation of ground and air transportation systems. Basic decision processes are examined that are used for cost analyses and planning (i.e, statistical decision theory, linear and dynamic programming, optimization, game theory). The effects on the environment and the community that a transportation system may have are discussed and modelled. Algorithmic structures are examined and selected bibliographic annotations are included. Transportation dynamic models were developed. Citizen participation in transportation projects (i.e, in Maryland and Massachusetts) is discussed. The relevance of the modelling and evaluation approaches to air transportation (i.e, airport planning) is examined in a case study in St. Louis, Missouri.

Haefner, L. E.↗
DOE OSTI2020

The Kalai-Smorodinsky solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the R package GPGame available on CRAN at https://cran.r-project.org/package=GPGame.

Game theory↗
NASA NTRS2004

Adaptive, Distributed Control of Constrained Multi-Agent Systems

Product Distribution (PO) theory was recently developed as a broad framework for analyzing and optimizing distributed systems. Here we demonstrate its use for adaptive distributed control of Multi-Agent Systems (MASS), i.e., for distributed stochastic optimization using MAS s. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (Probability dist&&on on the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. One common way to find that equilibrium is to have each agent run a Reinforcement Learning (E) algorithm. PD theory reveals this to be a particular type of search algorithm for minimizing the Lagrangian. Typically that algorithm i s quite inefficient. A more principled alternative is to use a variant of Newton's method to minimize the Lagrangian. Here we compare this alternative to RL-based search in three sets of computer experiments. These are the N Queen s problem and bin-packing problem from the optimization literature, and the Bar problem from the distributed RL literature. Our results confirm that the PD-theory-based approach outperforms the RL-based scheme in all three domains.

Bieniawski, Stefan↗
NASA NTRS2004

Product Distribution Theory for Control of Multi-Agent Systems

Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.

Lee, Chia Fan↗
NASA NTRS2004

Adaptive Multi-Agent Systems for Constrained Optimization

Product Distribution (PD) theory is a new framework for analyzing and controlling distributed systems. Here we demonstrate its use for distributed stochastic optimization. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. The updating of the Lagrange parameters in the Lagrangian can be viewed as a form of automated annealing, that focuses the MAS more and more on the optimal pure strategy. This provides a simple way to map the solution of any constrained optimization problem onto the equilibrium of a Multi-Agent System (MAS). We present computer experiments involving both the Queen s problem and K-SAT validating the predictions of PD theory and its use for off-the-shelf distributed adaptive optimization.

Macready, William↗
NASA NTRS2005

Distributed Optimization

We demonstrate a new framework for analyzing and controlling distributed systems, by solving constrained optimization problems with an algorithm based on that framework. The framework is ar. information-theoretic extension of conventional full-rationality game theory to allow bounded rational agents. The associated optimization algorithm is a game in which agents control the variables of the optimization problem. They do this by jointly minimizing a Lagrangian of (the probability distribution of) their joint state. The updating of the Lagrange parameters in that Lagrangian is a form of automated annealing, one that focuses the multi-agent system on the optimal pure strategy. We present computer experiments for the k-sat constraint satisfaction problem and for unconstrained minimization of NK functions.

Macready, William↗
DOE OSTI2020

A non-cooperative meta-modeling game for automated third-party calibrating, validating and falsifying constitutive laws with parallelized adversarial attacks

The evaluation of constitutive models, especially for high-risk and high-regret engineering applications, requires efficient and rigorous third-party calibration, validation and falsification. While there are numerous efforts to develop paradigms and standard procedures to validate models, difficulties may arise due to the sequential, manual, and often biased nature of the commonly adopted calibration and validation processes, thus slowing down data collections, hampering the progress towards discovering new physics, increasing expenses and possibly leading to misinterpretations of the credibility and application ranges of proposed models. This work attempts to introduce concepts from game theory and machine learning techniques to overcome many of these existing difficulties. Here, we introduce an automated meta-modeling game where two competing AI agents systematically generate experimental data to calibrate a given constitutive model and to explore its weakness such that the experiment design and model robustness can be improved through competitions. The two agents automatically search for the Nash equilibrium of the meta-modeling game in an adversarial reinforcement learning framework without human intervention. In particular, a protagonist agent seeks to find the more effective ways to generate data for model calibrations, while an adversary agent tries to find the most devastating test scenarios that expose the weaknesses of the constitutive model calibrated by the protagonist. By capturing all possible design options of the laboratory experiments into a single decision tree, we recast the design of experiments as a game of combinatorial moves that can be resolved through deep reinforcement learning by the two competing players. Our adversarial framework emulates idealized scientific collaborations and competitions among researchers to achieve a better understanding of the application range of the learned material laws and prevent misinterpretations caused by conventional AI-based third-party validation. Numerical examples are given to demonstrate the wide applicability of the proposed meta-modeling game with adversarial attacks on both human-crafted constitutive models and machine learning models.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Improving Simulated Annealing by Replacing Its Variables with Game-Theoretic Utility Maximizers

The game-theory field of Collective INtelligence (COIN) concerns the design of computer-based players engaged in a non-cooperative game so that as those players pursue their self-interests, a pre-specified global goal for the collective computational system is achieved as a side-effect. Previous implementations of COIN algorithms have outperformed conventional techniques by up to several orders of magnitude, on domains ranging from telecommunications control to optimization in congestion problems. Recent mathematical developments have revealed that these previously developed algorithms were based on only two of the three factors determining performance. Consideration of only the third factor would instead lead to conventional optimization techniques like simulated annealing that have little to do with non-cooperative games. In this paper we present an algorithm based on all three terms at once. This algorithm can be viewed as a way to modify simulated annealing by recasting it as a non-cooperative game, with each variable replaced by a player. This recasting allows us to leverage the intelligent behavior of the individual players to substantially improve the exploration step of the simulated annealing. Experiments are presented demonstrating that this recasting significantly improves simulated annealing for a model of an economic process run over an underlying small-worlds topology. Furthermore, these experiments reveal novel small-worlds phenomena, and highlight the shortcomings of conventional mechanism design in bounded rationality domains.

Wolpert, David H.↗