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Math-based reinforcement learning for the adaptive budgeted influence maximization problem

NETWORKS 2024年第3期83卷 547-569页

作者： Fadda, Edoardo Di Corso, Evelina Brusco, Davide Aelenei, Vlad Stefan Rares, Alexandru Balan Politecn Torino Dept Math Sci Turin Italy ISIRES Ist Italiano Ric & Sviluppo Turin Italy Politecn Torino Dept Math Sci Corso Duca Abruzzi 24 I-10129 Turin Italy

In social networks, the influence maximization problem requires selecting an initial set of nodes to influence so that the spread of influence can reach its maximum under certain diffusion models. Usually, the problem is formulated in a two-stage un-budgeted fashion: The decision maker selects a given number of nodes to influence and observes the results. In the adaptive version of the problem, it is possible to select the nodes at each time step of a given time interval. This allows the decision-maker to exploit the observation of the propagation and to make better decisions. This paper considers the adaptive budgeted influence maximization problem, that is, the adaptive problem in which the decision maker has a finite budget to influence the nodes, and each node requires a cost to be influenced. We present two solution techniques: The first is an approximated value iteration leveraging mixed integer linear problems while the second exploits new concepts from graph neural networks. Extensive numerical experiments demonstrate the effectiveness of the proposed approaches.

关键词： adaptive budgeted influence maximization problem approximate dynamic programming graph neural networks mixed integer linear problem reinforcement learning two-stage stochastic problem

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approximate optimal and safe coordination of nonlinear second-order multirobot systems with model uncertainties

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ISA TRANSACTIONS 2024年 149卷 155-167页

作者： Guo, Yaohua Huang, He Northwestern Polytech Univ 127 Youyi Rd Xian 710072 Shaanxi Peoples R China

This paper investigates the approximate optimal coordination for nonlinear uncertain second -order multirobot systems with guaranteed safety (collision avoidance) Through constructing novel local error signals, the collision -free control objective is formulated into an coordination optimization problem for nominal multirobot systems. Based on approximate dynamic programming technique, the optimal value functions and control policies are learned by simplified critic -only neural networks (NNs). Then, the approximated optimal controllers are redesigned using adaptive law to handle the effects of robots' uncertain dynamics. It is shown that the NN weights estimation errors are uniformly ultimately bounded under proper conditions, and safe coordination of multiple robots can be achieved regardless of model uncertainties. Numerical simulations finally illustrate the effectiveness of the proposed controller.

关键词： approximate dynamic programming Collision-free coordination Model uncertainties Multirobot systems

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Optimizing electrolyzer investments for green hydrogen production under market and technology uncertainties

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RENEWABLE ENERGY 2025年 249卷

作者： Trivella, Alessio Univ Twente Ind Engn & Business Informat Syst Hallenweg 17 NL-7522 NH Enschede Netherlands

Motivated by increasing curtailment of renewable energy, negative electricity prices, and growing importance of green hydrogen, many renewable energy producers are considering investing in electrolyzers to produce and sell green hydrogen. However, electrolyzers are still expensive technologies and their profitability is affected by uncertainties in electricity and hydrogen prices, investment cost, and curtailment levels, all of which fluctuate over time. In this paper, we study optimal electrolyzer investments as a real option problem where a renewable energy producer can decide over a planning horizon whether investing in an electrolyzer, its capacity, and whether to couple it with a storage system. Since the resulting dynamic stochastic optimization problem is intractable to solve to optimality, we leverage state-of-the-art approximate dynamic programming (ADP) methods to compute near-optimal investment policies and dual bounds. A computational study is conducted, offering insights into the investment option value under traditional and new ADP policies, and optimal investment decisions in relation to the evolution of the uncertainties, including the expected time to invest, asset size, and optimal electrolyzer utilization. The findings can be valuable for renewable energy producers interested in green hydrogen but lacking tools and insights to assess investment decisions in a complex and evolving energy landscape.

关键词： Real options Renewable energy Electrolyzer Green hydrogen Optimal investment approximate dynamic programming

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A Q-Learning Algorithm to Solve the Two-Player Zero-Sum Game Problem for Nonlinear Systems

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2025年第3期39卷 566-581页

作者： Islam, Afreen Chen, Anthony Siming Herrmann, Guido Univ Manchester Dept Elect & Elect Engn Manchester England

This paper deals with the two-player zero-sum game problem, which is a bounded L2$$ {L}_2 $$-gain robust control problem. Finding an analytical solution to the complex Hamilton-Jacobi-Issacs (HJI) equation is a challenging task. Hence, a novel Q-learning algorithm for unknown continuous-time (CT) affine-in-inputs nonlinear systems is proposed for generating an approximate solution to the HJI equation, which is valid in a local domain due to the use of a local approximator, that is, a Neural Network (NN) structure. The approach is model-free and does not require the knowledge of system drift dynamics, and input and disturbance gains. The algorithm learns online from measurements of state variables in real time. To generate the local approximate solution of the HJI equation for the two-player zero-sum game problem for nonlinear systems, the proposed non-iterative algorithm requires only a single critic NN instead of the commonly used triple NN approximator structure. A persistence of excitation condition is required to guarantee Uniformly Ultimately Boundedness (UUB) and convergence to the optimal solution. The effectiveness of the proposed Q-learning approach for the two-player zero-sum game problem is demonstrated via simulations of a linear F-16 aircraft plant and a highly complex nonlinear system. Proof of closed-loop system stability is provided using Lyapunov Analysis, and convergence of the approximate solution to the true saddle-point solution is guaranteed in a UUB-sense.

关键词： adaptive control approximate dynamic programming Q-learning zero-sum game

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Scheduling autonomous robots for an intralogistic application: A comparison of lookahead-based ADP strategies

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 271卷

作者： Battistotti, Margherita Brandimarte, Paolo Giancola, Francesca Mazzi, Nicolo Univ Manchester AMBS Booth St West Manchester M15 6PB England Politecn Torino DISMA Corso Duca Abruzzi 24 I-10129 Turin Italy Spindox Spa via Bisceglie 76 I-20152 Milan Italy Spindox Labs Srl via Cascata 56C I-38123 Trento Italy

The increasing role of e-commerce has spurred a significant amount of research on optimization in warehousing management, including routing and scheduling issues. When material handling is rigidly automated, a deterministic scheduling problem arises, for which solution strategies have been proposed in the literature. A recent trend is the introduction of autonomous robots, which may interact with human operators and offer additional flexibility in item manipulation. The resulting problem is affected by uncertainty, due to the interaction between robots and human workers and the possible failure in items manipulation. In the paper, we propose an adaptation of approximate dynamic programming strategies with limited lookahead, namely, rollout strategies and Monte Carlo tree search. The idea can be interpreted as an intermediate approach between the solution of a deterministic problem, disregarding uncertainty and using a long lookahead, or the application of pure state-based dispatching rules with no lookahead. The proposed approaches are compared against exact dynamic programming on small-size instances, and then evaluated on larger instances, proving their viability.

关键词： Intralogistics Scheduling approximate dynamic programming Rollout strategies Monte Carlo tree search

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Markdown Optimization via approximate dynamic programming

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2013年第1期6卷 64-78页

作者： Cosgun, Ozlem Kula, Ufuk Kahraman, Cengiz Fatih Univ Dept Ind Engn TR-34500 Istanbul Turkey Sakarya Univ Dept Ind Engn Sakarya Turkey Istanbul Tech Univ Dept Ind Engn TR-80626 Istanbul Turkey

We consider the markdown optimization problem faced by the leading apparel retail chain. Because of substitution among products the markdown policy of one product affects the sales of other products. Therefore, markdown policies for product groups having a significant crossprice elasticity among each other should be jointly determined. Since the state space of the problem is very huge, we use approximate dynamic programming. Finally, we provide insights on the behavior of how each product price affects the markdown policy.

关键词： approximate dynamic programming Multinomial logit model Cross-price elasticity Markdown optimization Pricing

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approximate dynamic programming Algorithms for Multidimensional Inventory Optimization Problems

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IFAC Proceedings Volumes 2013年第9期46卷 2015-2020页

作者： Mustafa Cimen Christopher Kirkbride Lancaster University Management School Lancaster LA1 4YX UK

An important issue in the supply chain literature concerns the optimization of inventory decisions. Single-product inventory problems are widely studied and have been optimally solved under a variety of assumptions. However, as supply chain systems become more complex, inventory decisions become more complicated for which the methods/approaches for optimizing single-product inventory systems are incapable of deriving optimal policies. Manufacturing process flexibility provides an example of such complex application areas. Interrelated products and production facilities form a highly multidimensional, non-decomposable system for which optimal policies cannot be obtained by classical methods. We propose the methodology of approximate dynamic programming (ADP) to overcome the computational challenge imposed by this multidimensionality. Incorporating a sample backup approach, ADP develops policies by utilizing only a fraction of the computations required by classical dynamic programming. However, there are no studies in the literature that optimize production decisions in a stochastic, multifactory, multiproduct inventory system of this complexity. This paper aims to explore the feasibility of ADP algorithms for this application. We present the results from a series of numerical experiments that establish the strong performance of policies developed via temporal difference ADP algorithms in comparison to optimal policies.

关键词： approximate dynamic programming dynamic programming flexible manufacturing systems inventory control Markov decision problems process flexibility simulation optimization

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Leveraging Time-Causal State Variable Aggregation for Real-Time Schedule of Massive Air Conditioners

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IEEE TRANSACTIONS ON SMART GRID 2025年第3期16卷 2389-2403页

作者： Liu, Jingguan Ai, Xiaomeng Cui, Shichang Xue, Xizhen Wang, Shengshi Fang, Jiakun Wen, Jinyu Shi, Yang Huazhong Univ Sci & Technol State Key Lab Adv Electromagnet Technol Wuhan 430074 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Univ Victoria Dept Mech Engn Victoria BC V8W 3P1 Canada

Air conditioner (AC) loads offer promising flexibility for active distribution networks to manage uncertainties, such as those in renewable energy generation, electricity prices, and load demand. However, real-time scheduling of ACs is challenging due to their massive temporal coupling constraints and time-causal uncertainties. To address this, a novel time-causal aggregation-based approximate dynamic programming (TCA-ADP) algorithm is proposed for efficient scheduling. The time-causality requirements for aggregating state variables are first analyzed to align with the real-time sequential decision-making process. Subsequently, an enhanced aggregation model is developed to ensure both high accuracy and adherence to time causality. The aggregation process is further reformulated as a linear program to optimize aggregation parameters and enable tractable computation. Accordingly, the TCA-ADP leverages aggregated state variables to approximate the value function as a new way, balancing computational efficiency and economy against the large value function space of massive ACs. By training the value function offline using historical data, the TCA-ADP efficiently achieves near-optimal real-time scheduling of massive ACs through parallel and closed-form disaggregation. Case studies demonstrate the effectiveness and scalability of the TCA-ADP, highlighting its aggregation accuracy, uncertainty handling, and the trade-off between economy and tractability.

关键词： Real-time systems Uncertainty Heuristic algorithms Cause effect analysis Training dynamic programming Approximation algorithms Inverters Accuracy Renewable energy sources Air conditioner state variable aggregation real-time scheduling approximate dynamic programming

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Planning Versus Learning: Fair Space-Time Scheduling for Unwired Networks

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2024年第11期23卷 16621-16634页

作者： Peng, Chen Mitra, Urbashi Univ Southern Calif Dept Elect & Comp Engn Los Angeles CA 90089 USA

Space-time scheduling for multi-user networks under fairness considerations is investigated. Scheduling is formulated as a sequential decision-making problem under the Markov Decision Processes (MDP) framework. Although the initial focus of the work is underwater acoustic networks, the proposed strategies are also validated for terrestrial radio frequency networks. If environment exploration is expensive, planning is more efficient than online learning. A challenge of the proportional fairness is that the additive structure between current and future rewards does not hold. An approximate reward function that is additive is proposed, enabling dynamic programming. Computational complexity is addressed through sample-based approximations. Error accumulation and error bounds are analyzed to show that error decays with time. As mobility induces model-shifts, a novel re-planning scheme is proposed to optimize the timings of policy updates. Numerical results show that the proposed scheme significantly improves network capacity while maintaining a high level of fairness. Furthermore, the proposed approach yields average capacity and fairness gains as high as 37% and 27%, respectively, compared to current approaches.

关键词： Underwater acoustics Planning Radio frequency Array signal processing Numerical models Multiaccess communication Mathematical models Network scheduling fairness Markov decision process approximate dynamic programming

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Policy Iteration for Optimal Control of Discrete-Time Time-Varying Nonlinear Systems

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IEEE/CAA Journal of Automatica Sinica 2023年第3期10卷 781-791页

作者： Guangyu Zhu Xiaolu Li Ranran Sun Yiyuan Yang Peng Zhang Beijing Research Center of Urban Traffic Information Sensing and Service Technologies Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport Beijing Jiaotong UniversityBeijing 100044China Transport Planning and Research Institute Ministry of TransportChinaBeijing 100028China

Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems,in this paper,a new iterative adaptive dynamic programming algorithm,which is the discrete-time time-varying policy iteration(DTTV)algorithm,is *** iterative control law is designed to update the iterative value function which approximates the index function of optimal *** admissibility of the iterative control law is *** results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal *** implement the algorithm,neural networks are employed and a new implementation structure is established,which avoids solving the generalized Bellman equation in each ***,the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm,where the mass and pendulum bar length are permitted to be time-varying *** effectiveness of the developed method is illustrated by numerical results and comparisons.

关键词： Adaptive critic designs adaptive dynamic programming approximate dynamic programming optimal control policy iteration time-varying

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