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Learning Nash Equilibria in Monotone Games

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arXiv 2019年

作者： Tatarenko, Tatiana Kamgarpour, Maryam Control Methods and Robotics Lab Technical University Darmstadt Darmstadt64283 Germany Automatic Control Laboratory ETH Zürich Switzerland

—We consider multi-agent decision making where each agent’s cost function depends on all agents’ strategies. We propose a distributed algorithm to learn a Nash equilibrium, whereby each agent uses only obtained values of her cost function at each joint played action, lacking any information of the functional form of her cost or other agents’ costs or strategy sets. In contrast to past work where convergent algorithms required strong monotonicity, we prove algorithm convergence under mere monotonicity assumption. This significantly widens algorithm’s applicability, such as to games with linear coupling constraints. Copyright © 2019, The Authors. All rights reserved.

关键词： Cost functions

Domain Mixture: An Overlooked Scenario in Domain Adaptation

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Domain Mixture: An Overlooked Scenario in Domain Adaptation

International Conference on Machine Learning and Applications (ICMLA)

作者： Sebastian Schrom Stephan Hasler Control Methods & Robotics Lab TU Darmstadt Darmstadt Germany Honda Research Institute GmbH Offenbach/Main Germany

An image based object classification system trained on one domain usually shows decreased performance for other domains if data distributions differ significantly. There exist various domain adaptation approaches that improve generalization between domains. However, those approaches consider during transfer only the restricted setting where supervised samples of all competing classes are available from the source domain. We investigate here the more open and so far overlooked scenario, where during training only a subset of all competing classes is shown in one domain and another subset in another domain. We show the unexpected tendency of a deep learning classifier to use the domain origin as a prominent feature, which is resulting in a poor performance when testing on samples of unseen domain-class combinations. With an existing domain adaptation method this issue can be overcome, while additional unsupervised data of all unseen domain-class combinations is not essential. First results of this overlooked scenario are extensively discussed on a modified MNIST benchmark.

关键词： Training Standards Feature extraction Robots Machine learning Task analysis Optimization

A Foresighted Driver Model derived from Integral Expected Risk

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A Foresighted Driver Model derived from Integral Expected Ri...

International Conference on Intelligent Transportation

作者： Julian Eggert Fabian Mueller Honda Research Institute (HRI) Europe Offenbach/Main Germany Control Methods and Robotics Lab Technical University of Darmstadt Darmstadt Germany

ISBN: (纸本)9781538670255

Current efforts in Advanced Driver Assistant Systems and Autonomous Driving research target at making the vehicles more intelligent, in terms of understanding what is going on and selecting the most appropriate behaviors. A crucial element of this research is the prediction of the evolution of the current driving situation with microscopic driver models. In this paper we present a microscopic driver model with a gradient-like, simple behavior generation that is fully and concisely derived from mathematical risk theory. Following this model, drivers act by estimating the expected, integral future risks and benefits and by seeking the best instantaneous tradeoff between these quantities, choosing the immediate action that reduces the hypothetical risks in the most efficient way. We show how this model is able to incorporate different risk types and situation parameters, allowing an extension and generalization to variable scenarios.

关键词： Vehicles Uncertainty Predictive models Adaptation models Trajectory Microscopy

Geometric convergence of distributed gradient play in games with unconstrained action sets

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arXiv 2019年

作者： Tatarenko, Tatiana Nedić, Angelia Control Methods and Robotics Lab TU darmstadt Germany School of Electrical Computer and Energy Engineering Arizona State University United States

We provide a distributed algorithm to learn a Nash equilibrium in a class of non-cooperative games with strongly monotone mappings and unconstrained action sets. Each player has access to her own smooth local cost function and can communicate to her neighbors in some undirected graph. We consider a distributed communication-based gradient algorithm. For this procedure, we prove geometric convergence to a Nash equilibrium. In contrast to our previous works [15], [16], where the proposed algorithms required two parameters to be set up and the analysis was based on a so called augmented game mapping, the procedure in this work corresponds to a standard distributed gradient play and, thus, only one constant step size parameter needs to be chosen appropriately to guarantee fast convergence to a game solution. Moreover, we provide a rigorous comparison between the convergence rate of the proposed distributed gradient play and the rate of the GRANE algorithm presented in [15]. It allows us to demonstrate that the distributed gradient play outperforms the GRANE in terms of convergence speed. Copyright © 2019, The Authors. All rights reserved.

关键词： Game theory

Self-Validation for Automotive Visual Odometry

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Self-Validation for Automotive Visual Odometry

IEEE Symposium on Intelligent Vehicle

作者： Martin Buczko Volker Willert Julian Schwehr Jurgen Adamy Control Methods & Robotics Lab TU Darmstadt Germany

Automotive visual odometry has become a highly researched topic. The published works have turned cameras into a very precise source of ego motion estimation. However, for automotive application, visual odometry has to be integrated into a sensor fusion to simultaneously obtain global localization, maximum availability as well as highest precision. Since any visual odometry remains sensitive to its environment, good motion estimation cannot always be guaranteed. Consequently, a self-validation scheme is one of the barriers towards application in a sensor fusion system. In order to solve this problem, we first formulate an Ackermann vehicle's motion as a function of its forward speed and yaw rate. Secondly, we present a data-driven model, which achieves to reconstruct the sideward speed as a function of the yaw rate only. As we show, both models reach the quality of the estimated sideward motion from visual odometry. The therewith achieved redundancy can be used for different tasks. Of course, the estimation of the sideward motion can be excluded from the visual odometry scheme to save computation time. This is of special interest for monocular systems, where yet no absolute scale of a translation motion could be directly calculated. Instead, we propose to maintain the estimation of the sideward motion in the visual odometry and to compare the result to the modeled motion. As we show, the emerging deviation is a very good metric for self-validation of the overall visual odometry estimate. Integrating the resulting method into our visual odometry system, we currently achieve the best frame-to-frame result in the KITTI benchmark.

关键词： Visual odometry Motion estimation Adaptive optics Optical imaging Cameras Sensor fusion Robot sensing systems

Stochastic Learning in Potential Games: Communication and Payoff-Based Approaches

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arXiv 2018年

作者： Tatarenko, Tatiana Control Methods and Robotics Lab Technical University Darmstadt Darmstadt Germany

Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function coincides with a global objective function to be maximized. In this approach, the agents correspond to the strategic decision makers and the optimization problem is equivalent to the problem of learning a potential function maximizer in the designed game. The paper deals with two different information settings in the system. Firstly, we consider systems, where agents have the access to the gradient of their utility functions. However, they do not possess the full information about the joint actions. Thus, to be able to move along the gradient toward a local optimum, they need to exchange the information with their neighbors by means of communication. The second setting refers to a payoff-based approach to learning potential function maximizers. Here, we assume that at each iteration agents can only observe their own played actions and experienced payoffs. In both cases, the paper studies unconstrained nonconvex optimization with a differentiable objective function. To develop the corresponding algorithms guaranteeing convergence to a local maximum of the potential function in the game, we utilize the idea of the well-known Robbins-Monro procedure based on the theory of stochastic approximation. Copyright © 2018, The Authors. All rights reserved.

关键词： Multi agent systems

Time-Invariant control in LQ Optimal Tracking: An Alternative to Output Regulation

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IFAC-PapersOnLine 2017年第1期50卷 4912-4919页

作者： Bernhard S. Institute of Automatic Control Control Methods & Robotics Lab Technische Universität Darmstadt Darmstadt 64283 Germany

We propose a new time-invariant control for linear quadratic tracking problems with references and disturbances generated by linear exo-systems. The control consists of a static feedback and a static pre-filter similar as in output regulation theory (ORT). Instead of forcing the tracking error to converge to zero, a tolerated steady-state error is balanced against the necessary input-energy via a quadratic cost. For the first time in this context, we deduce a time-invariant control from algebraic equations such that necessary optimality conditions are satisfied on infinite horizons. Then, we prove strong optimality for bounded exo-system states. Hence, any other steady-state solution will lead to infinite additional cost. On finite horizons and for arbitrary exo-systems, we prove that our control is an agreeable plan as it approximates the computational expensive, time-varying optimal control of any suitably large horizon. Since our control applies for any initial conditions of the plant and the exo-system, it is well suited for a practical resource-efficient implementation. In this regard, a presented algorithm allows for an easy to carry out control design. Finally, an industrial application indicates the unified treatment of square, under- and over-actuated systems by our approach in contrast to ORT. © 2017

关键词： Agreeable Plans Disturbances Linear Quadratic Linear Systems Optimal Tracking Output Regulation Over-Actuated Time-Varying References Under-Actuated

Optimal output regulation for square, over-actuated and under-actuated linear systems

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arXiv 2018年

作者： Bernhard, Sebastian Adamy, Jürgen Institute of Automatic Control and Mechatronics Control Methods and Robotics Lab Technische Universität Darmstadt Landgraf-Georg Str. 4 Darmstadt64283 Germany

This paper considers two different problems in trajectory tracking control for linear systems. First, if the control is not unique which is most input energy efficient. Second, if exact tracking is infeasible which control performs most accurately. These are typical challenges for over-actuated systems and for under-actuated systems, respectively. We formulate both goals as optimal output regulation problems. Then we contribute two new sets of regulator equations to output regulation theory that provide the desired solutions. A thorough study indicates solvability and uniqueness under weak assumptions. E.g., we can always determine the solution of the classical regulator equations that is most input energy efficient. This is of great value if there are infinitely many solutions. We derive our results by a linear quadratic tracking approach and establish a useful link to output regulation theory. Copyright © 2018, The Authors. All rights reserved.

关键词： Linear systems

Efficient global localization using vision and digital offline map

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Efficient global localization using vision and digital offli...

International Conference on Intelligent Transportation

作者： Martin Buczko Volker Willert Control Methods & Robotics Lab TU Darmstadt Germany

ISBN: (纸本)9781538615270

We present an efficient method that combines visual odometry and offline map data for global localization. In contrast to other approaches, no further sensor as GPS or precise information on the initial pose is needed. Rough localization information like the current city or region can be used to speed up the initialization, but is not required. The proposed method uses the observation of street signs in a twofold manner: To roughly pre-localize the vehicle and to subsequently transform the three-dimensional vehicle-to-map-alignment-task into a one-dimensional search within a closed interval. This leads to a fast matching method, that finds the proper shift and rotation angle between the planar trajectory of the visual odometry and the offline map data. The method is evaluated on a real trajectory that is computed with a state-of-the-art visual odometry system to demonstrate its performance.

关键词： Trajectory Visual odometry Optical character recognition software Global Positioning System Image reconstruction Conferences