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Reinforcement learning

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Full-Text Articles in Artificial Intelligence and Robotics

Towards An Active Foveated Approach To Computer Vision, Dario Dematties, Silvio Rizzi, George K. Thiruvathukal, Alejandro Javier Wainselboim Jan 2022

Towards An Active Foveated Approach To Computer Vision, Dario Dematties, Silvio Rizzi, George K. Thiruvathukal, Alejandro Javier Wainselboim

Computer Science: Faculty Publications and Other Works

In this paper, a series of experimental methods are presented explaining a new approach towards active foveated Computer Vision (CV). This is a collaborative effort between researchers at CONICET Mendoza Technological Scientific Center from Argentina, Argonne National Laboratory (ANL), and Loyola University Chicago from the US. The aim is to advance new CV approaches more in line with those found in biological agents in order to bring novel solutions to the main problems faced by current CV applications. Basically this work enhance Self-supervised (SS) learning, incorporating foveated vision plus saccadic behavior in order to improve training and computational efficiency without …


Hierarchical Control Of Multi-Agent Reinforcement Learning Team In Real-Time Strategy (Rts) Games, Weigui Jair Zhou, Budhitama Subagdja, Ah-Hwee Tan, Darren Wee Sze Ong Dec 2021

Hierarchical Control Of Multi-Agent Reinforcement Learning Team In Real-Time Strategy (Rts) Games, Weigui Jair Zhou, Budhitama Subagdja, Ah-Hwee Tan, Darren Wee Sze Ong

Research Collection School Of Computing and Information Systems

Coordinated control of multi-agent teams is an important task in many real-time strategy (RTS) games. In most prior work, micromanagement is the commonly used strategy whereby individual agents operate independently and make their own combat decisions. On the other extreme, some employ a macromanagement strategy whereby all agents are controlled by a single decision model. In this paper, we propose a hierarchical command and control architecture, consisting of a single high-level and multiple low-level reinforcement learning agents operating in a dynamic environment. This hierarchical model enables the low-level unit agents to make individual decisions while taking commands from the high-level …


Dqn-Based Path Planning Method And Simulation For Submarine And Warship In Naval Battlefield, Xiaodong Huang, Haitao Yuan, Bi Jing, Liu Tao Oct 2021

Dqn-Based Path Planning Method And Simulation For Submarine And Warship In Naval Battlefield, Xiaodong Huang, Haitao Yuan, Bi Jing, Liu Tao

Journal of System Simulation

Abstract: To realize multi-agent intelligent planning and target tracking in complex naval battlefield environment, the work focuses on agents (submarine or warship), and proposes a simulation method based on reinforcement learning algorithm called Deep Q Network (DQN). Two neural networks with the same structure and different parameters are designed to update real and predicted Q values for the convergence of value functions. An ε-greedy algorithm is proposed to design an action selection mechanism, and a reward function is designed for the naval battlefield environment to increase the update velocity and generalization ability of Learning with Experience Replay (LER). Simulation results …


Research On Experimental Method Of Joint Operation Simulation Based On Human-Machine Hybrid Intelligence, Ma Jun, Jingyu Yang, Wu Xi Oct 2021

Research On Experimental Method Of Joint Operation Simulation Based On Human-Machine Hybrid Intelligence, Ma Jun, Jingyu Yang, Wu Xi

Journal of System Simulation

Abstract: In view of the difficulties that the joint operation simulation experiment methods are mainly for guiding equipment evaluation and demonstration, which is difficult to effectively support the research of operation problems, a joint operation simulation experiment method based on human-machine hybrid intelligence is proposed. The classification, generation and accumulation process of the knowledge in joint operation simulation experiment are clarified. Through the detailed descriptions of experimental interaction process, experimental operation process, experimental driving mode, simulation operation mode, supporting system structure, etc., a joint operation simulation experiment framework based on man-machine hybrid intelligence is constructed. It provides a new method …


Study On Next-Generation Strategic Wargame System, Wu Xi, Xianglin Meng, Jingyu Yang Sep 2021

Study On Next-Generation Strategic Wargame System, Wu Xi, Xianglin Meng, Jingyu Yang

Journal of System Simulation

Abstract: Strategic wargame is an important support to the strategic decision. The research status and challenges of the strategic wargame are analyzed, and the influence of big data and artificial intelligence technology on the strategic wargame system is studied. The prospects and key technologies of the next-generation strategic wargame system are studied, including the construction of event association graph for strategic topics, generation of strategic decision sparse samples based on generative adversarial nets, gaming strategy learning of human-in-loop hybrid enhancement, and public opinion dissemination modeling technology based on social network. The development trend of the strategic wargame is proposed.


Self-Learning-Based Multiple Spacecraft Evasion Decision Making Simulation Under Sparse Reward Condition, Zhao Yu, Jifeng Guo, Yan Peng, Chengchao Bai Aug 2021

Self-Learning-Based Multiple Spacecraft Evasion Decision Making Simulation Under Sparse Reward Condition, Zhao Yu, Jifeng Guo, Yan Peng, Chengchao Bai

Journal of System Simulation

Abstract: In order to improve the ability of spacecraft formation to evade multiple interceptors, aiming at the low success rate of traditional procedural maneuver evasion, a multi-agent cooperative autonomous decision-making algorithm, which is based on deep reinforcement learning method, is proposed. Based on the actor-critic architecture, a multi-agent reinforcement learning algorithm is designed, in which a weighted linear fitting method is proposed to solve the reliability allocation problem of the self-learning system. To solve the sparse reward problem in task scenario, a sparse reward reinforcement learning method based on inverse value method is proposed. According to the task scenario, …


Identification Of Chemical Structures And Substructures Via Deep Q-Learning And Supervised Learning Of Ftir Spectra, Joshua D. Ellis Aug 2021

Identification Of Chemical Structures And Substructures Via Deep Q-Learning And Supervised Learning Of Ftir Spectra, Joshua D. Ellis

Graduate Theses/Dissertations

Fourier-transform infrared (FTIR) spectra of organic compounds can be used to compare and identify compounds. A mid-FTIR spectrum gives absorbance values of a compound over the 400-4000 cm-1 range. Spectral matching is the process of comparing the spectral signature of two or more compounds and returning a value for the similarity of the compounds based on how closely their spectra match. This process is commonly used to identify an unknown compound by searching for its spectrum’s closes match in a database of known spectra. A major limitation of this process is that it can only be used to identify …


High-Density Parking For Autonomous Vehicles., Parag J. Siddique Aug 2021

High-Density Parking For Autonomous Vehicles., Parag J. Siddique

Electronic Theses and Dissertations

In a common parking lot, much of the space is devoted to lanes. Lanes must not be blocked for one simple reason: a blocked car might need to leave before the car that blocks it. However, the advent of autonomous vehicles gives us an opportunity to overcome this constraint, and to achieve a higher storage capacity of cars. Taking advantage of self-parking and intelligent communication systems of autonomous vehicles, we propose puzzle-based parking, a high-density design for a parking lot. We introduce a novel method of vehicle parking, which leads to maximum parking density. We then propose a heuristic method …


Learning To Assign: Towards Fair Task Assignment In Large-Scale Ride Hailing, Dingyuan Shi, Yongxin Tong, Zimu Zhou, Bingchen Song, Weifeng Lv, Qiang Yang Aug 2021

Learning To Assign: Towards Fair Task Assignment In Large-Scale Ride Hailing, Dingyuan Shi, Yongxin Tong, Zimu Zhou, Bingchen Song, Weifeng Lv, Qiang Yang

Research Collection School Of Computing and Information Systems

Ride hailing is a widespread shared mobility application where the central issue is to assign taxi requests to drivers with various objectives. Despite extensive research on task assignment in ride hailing, the fairness of earnings among drivers is largely neglected. Pioneer studies on fair task assignment in ride hailing are ineffective and inefficient due to their myopic optimization perspective and timeconsuming assignment techniques. In this work, we propose LAF, an effective and efficient task assignment scheme that optimizes both utility and fairness. We adopt reinforcement learning to make assignments in a holistic manner and propose a set of acceleration techniques …


Learning Index Policies For Restless Bandits With Application To Maternal Healthcare, Arpita Biswas, Gaurav Aggarwal, Pradeep Varakantham, Milind Tambe May 2021

Learning Index Policies For Restless Bandits With Application To Maternal Healthcare, Arpita Biswas, Gaurav Aggarwal, Pradeep Varakantham, Milind Tambe

Research Collection School Of Computing and Information Systems

In many community health settings, it is crucial to have a systematic monitoring and intervention process to ensure that the patients adhere to healthcare programs, such as periodic health checks or taking medications. When these interventions are expensive, they can be provided to only a fixed small fraction of the patients at any period of time. Hence, it is important to carefully choose the beneficiaries who should be provided with interventions and when. We model this scenario as a restless multi-armed bandit (RMAB) problem, where each beneficiary is assumed to transition from one state to another depending on the intervention …


Approximate Difference Rewards For Scalable Multigent Reinforcement Learning, Arambam James Singh, Akshat Kumar, Hoong Chuin Lau May 2021

Approximate Difference Rewards For Scalable Multigent Reinforcement Learning, Arambam James Singh, Akshat Kumar, Hoong Chuin Lau

Research Collection School Of Computing and Information Systems

We address the problem ofmultiagent credit assignment in a large scale multiagent system. Difference rewards (DRs) are an effective tool to tackle this problem, but their exact computation is known to be challenging even for small number of agents. We propose a scalable method to compute difference rewards based on aggregate information in a multiagent system with large number of agents by exploiting the symmetry present in several practical applications. Empirical evaluation on two multiagent domains - air-traffic control and cooperative navigation, shows better solution quality than previous approaches.


Playing Pong Using Q-Learning, Akash Kumar Jan 2021

Playing Pong Using Q-Learning, Akash Kumar

West Chester University Master’s Theses

This thesis involves the use of a reinforcement learning algorithm (RL) called Q-learning to train a Q-agent to play a game of Pong against a near-perfect opponent. Compared to previously related work which trained Pong RL agents by combining Q-learning with deep learning in an algorithm known as Deep Q-Networks, the work presented in this paper takes advantage of known environment constraints of the custom-made Pong environment to train the agent using one-step Q-learning alone. In addition, the thesis explores ways of making the Q-learning more efficient by converting Markov Decision Processes (MDPs) to Partially Observable Markov Decision Processes (POMDPs), …


Markov Decision Processes With Embedded Agents, Luke Harold Miles Jan 2021

Markov Decision Processes With Embedded Agents, Luke Harold Miles

Theses and Dissertations--Computer Science

We present Markov Decision Processes with Embedded Agents (MDPEAs), an extension of multi-agent POMDPs that allow for the modeling of environments that can change the actuators, sensors, and learning function of the agent, e.g., a household robot which could gain and lose hardware from its frame, or a sovereign software agent which could encounter viruses on computers that modify its code. We show several toy problems for which standard reinforcement-learning methods fail to converge, and give an algorithm, `just-copy-it`, which learns some of them. Unlike MDPs, MDPEAs are closed systems and hence their evolution over time can be treated as …


Reinforcement Learning For Zone Based Multiagent Pathfinding Under Uncertainty, Jiajing Ling, Tarun Gupta, Akshat Kumar Oct 2020

Reinforcement Learning For Zone Based Multiagent Pathfinding Under Uncertainty, Jiajing Ling, Tarun Gupta, Akshat Kumar

Research Collection School Of Computing and Information Systems

We address the problem of multiple agents finding their paths from respective sources to destination nodes in a graph (also called MAPF). Most existing approaches assume that all agents move at fixed speed, and that a single node accommodates only a single agent. Motivated by the emerging applications of autonomous vehicles such as drone traffic management, we present zone-based path finding (or ZBPF) where agents move among zones, and agents' movements require uncertain travel time. Furthermore, each zone can accommodate multiple agents (as per its capacity). We also develop a simulator for ZBPF which provides a clean interface from the …


Learning To Collaborate In Multi-Module Recommendation Via Multi-Agent Reinforcement Learning Without Communication, Xu He, An Bo, Yanghua Li, Haikai Chen, Rundong Wang, Xinrun Wang, Runsheng Yu, Xin Li, Zhirong Wang Sep 2020

Learning To Collaborate In Multi-Module Recommendation Via Multi-Agent Reinforcement Learning Without Communication, Xu He, An Bo, Yanghua Li, Haikai Chen, Rundong Wang, Xinrun Wang, Runsheng Yu, Xin Li, Zhirong Wang

Research Collection School Of Computing and Information Systems

With the rise of online e-commerce platforms, more and more customers prefer to shop online. To sell more products, online platforms introduce various modules to recommend items with different properties such as huge discounts. A web page often consists of different independent modules. The ranking policies of these modules are decided by different teams and optimized individually without cooperation, which might result in competition between modules. Thus, the global policy of the whole page could be sub-optimal. In this paper, we propose a novel multi-agent cooperative reinforcement learning approach with the restriction that different modules cannot communicate. Our contributions are …


Allosteric Regulation At The Crossroads Of New Technologies: Multiscale Modeling, Networks, And Machine Learning, Gennady M. Verkhivker, Steve Agajanian, Guang Hu, Peng Tao Jul 2020

Allosteric Regulation At The Crossroads Of New Technologies: Multiscale Modeling, Networks, And Machine Learning, Gennady M. Verkhivker, Steve Agajanian, Guang Hu, Peng Tao

Mathematics, Physics, and Computer Science Faculty Articles and Research

Allosteric regulation is a common mechanism employed by complex biomolecular systems for regulation of activity and adaptability in the cellular environment, serving as an effective molecular tool for cellular communication. As an intrinsic but elusive property, allostery is a ubiquitous phenomenon where binding or disturbing of a distal site in a protein can functionally control its activity and is considered as the “second secret of life.” The fundamental biological importance and complexity of these processes require a multi-faceted platform of synergistically integrated approaches for prediction and characterization of allosteric functional states, atomistic reconstruction of allosteric regulatory mechanisms and discovery of …


Joint Optimization Control Of Energy Storage System Management And Demand Response, Xueying Gao, Tang Hao, Gangzhong Miao, Zhaowu Ping Jul 2020

Joint Optimization Control Of Energy Storage System Management And Demand Response, Xueying Gao, Tang Hao, Gangzhong Miao, Zhaowu Ping

Journal of System Simulation

Abstract: The joint optimization problem of energy management and demand response were studied in order to reduce the long-run cost of electricity users equipped with energy storage unit and smart applications, and to increase their benefits meanwhile. The goals were achieved by controlling both the energy storage unit (charging, discharging, or idle) and the load service (access or delay). Based on the random nature of solar photovoltaic, load demand electricity and electricity price, the joint optimization problem was modeled as infinite-horizon Markov decision process model, and Q-learning algorithm was proposed to find the optimal solution. Simulation results show that the …


Analysis And Optimization Of The Action Chain Mechanism In Agent2d Underlying In Robocup2d Soccer League, Chen Bing, Feifan Xu, Hanyan Xu, Zekai Cheng, Liu Cheng Jun 2020

Analysis And Optimization Of The Action Chain Mechanism In Agent2d Underlying In Robocup2d Soccer League, Chen Bing, Feifan Xu, Hanyan Xu, Zekai Cheng, Liu Cheng

Journal of System Simulation

Abstract: In the RoboCup2D soccer league, Agent2D is one of the most widely used underlying team in China. Data transmission noise and the incomplete action chain mechanism make the underlying teams using Agent2D be lack of flexibility. This paper introduces an action correcting parameter and optimizes the operation of the action chain by reinforcement learning mechanism. The performance of the Agent2D underlying team is improved in the game and the adaptability of the team is enhanced. Simulation experiment results show that this method has a certain effect.


Monte Carlo Tree Search Applied To A Modified Pursuit/Evasion Scotland Yard Game With Rendezvous Spaceflight Operation Applications, Joshua A. Daughtery Jun 2020

Monte Carlo Tree Search Applied To A Modified Pursuit/Evasion Scotland Yard Game With Rendezvous Spaceflight Operation Applications, Joshua A. Daughtery

Theses and Dissertations

This thesis takes the Scotland Yard board game and modifies its rules to mimic important aspects of space in order to facilitate the creation of artificial intelligence for space asset pursuit/evasion scenarios. Space has become a physical warfighting domain. To combat threats, an understanding of the tactics, techniques, and procedures must be captured and studied. Games and simulations are effective tools to capture data lacking historical context. Artificial intelligence and machine learning models can use simulations to develop proper defensive and offensive tactics, techniques, and procedures capable of protecting systems against potential threats. Monte Carlo Tree Search is a bandit-based …


Using Taint Analysis And Reinforcement Learning (Tarl) To Repair Autonomous Robot Software, Damian Lyons, Saba Zahra May 2020

Using Taint Analysis And Reinforcement Learning (Tarl) To Repair Autonomous Robot Software, Damian Lyons, Saba Zahra

Faculty Publications

It is important to be able to establish formal performance bounds for autonomous systems. However, formal verification techniques require a model of the environment in which the system operates; a challenge for autonomous systems, especially those expected to operate over longer timescales. This paper describes work in progress to automate the monitor and repair of ROS-based autonomous robot software written for an a-priori partially known and possibly incorrect environment model. A taint analysis method is used to automatically extract the data-flow sequence from input topic to publish topic, and instrument that code. A unique reinforcement learning approximation of MDP utility …


Applying Imitation And Reinforcement Learning To Sparse Reward Environments, Haven Brown May 2020

Applying Imitation And Reinforcement Learning To Sparse Reward Environments, Haven Brown

Computer Science and Computer Engineering Undergraduate Honors Theses

The focus of this project was to shorten the time it takes to train reinforcement learning agents to perform better than humans in a sparse reward environment. Finding a general purpose solution to this problem is essential to creating agents in the future capable of managing large systems or performing a series of tasks before receiving feedback. The goal of this project was to create a transition function between an imitation learning algorithm (also referred to as a behavioral cloning algorithm) and a reinforcement learning algorithm. The goal of this approach was to allow an agent to first learn to …


Hierarchical Multiagent Reinforcement Learning For Maritime Traffic Management, Arambam James Singh, Akshat Kumar, Hoong Chuin Lau May 2020

Hierarchical Multiagent Reinforcement Learning For Maritime Traffic Management, Arambam James Singh, Akshat Kumar, Hoong Chuin Lau

Research Collection School Of Computing and Information Systems

Increasing global maritime traffic coupled with rapid digitization and automation in shipping mandate developing next generation maritime traffic management systems to mitigate congestion, increase safety of navigation, and avoid collisions in busy and geographically constrained ports (such as Singapore's). To achieve these objectives, we model the maritime traffic as a large multiagent system with individual vessels as agents, and VTS (Vessel Traffic Service) authority as a regulatory agent. We develop a hierarchical reinforcement learning approach where vessels first select a high level action based on the underlying traffic flow, and then select the low level action that determines their future …


Deep Reinforcement Learning For The Optimization Of Building Energy Control And Management, Jun Hao Jan 2020

Deep Reinforcement Learning For The Optimization Of Building Energy Control And Management, Jun Hao

Electronic Theses and Dissertations

Most of the current game-theoretic demand-side management methods focus primarily on the scheduling of home appliances, and the related numerical experiments are analyzed under various scenarios to achieve the corresponding Nash-equilibrium (NE) and optimal results. However, not much work is conducted for academic or commercial buildings. The methods for optimizing academic-buildings are distinct from the optimal methods for home appliances. In my study, we address a novel methodology to control the operation of heating, ventilation, and air conditioning system (HVAC).

We assume that each building in our campus is equipped with smart meter and communication system which is envisioned in …


Wind Power Forecasting Methods Based On Deep Learning: A Survey, Xing Deng, Haijian Shao, Chunlong Hu, Dengbiao Jiang, Yingtao Jiang Jan 2020

Wind Power Forecasting Methods Based On Deep Learning: A Survey, Xing Deng, Haijian Shao, Chunlong Hu, Dengbiao Jiang, Yingtao Jiang

Electrical & Computer Engineering Faculty Research

Accurate wind power forecasting in wind farm can effectively reduce the enormous impact on grid operation safety when high permeability intermittent power supply is connected to the power grid. Aiming to provide reference strategies for relevant researchers as well as practical applications, this paper attempts to provide the literature investigation and methods analysis of deep learning, enforcement learning and transfer learning in wind speed and wind power forecasting modeling. Usually, wind speed and wind power forecasting around a wind farm requires the calculation of the next moment of the definite state, which is usually achieved based on the state of …


Satellite Constellation Deployment And Management, Joseph Ryan Kopacz Jan 2020

Satellite Constellation Deployment And Management, Joseph Ryan Kopacz

Electronic Theses and Dissertations

This paper will review results and discuss a new method to address the deployment and management of a satellite constellation. The first two chapters will explorer the use of small satellites, and some of the advances in technology that have enabled small spacecraft to maintain modern performance requirements in incredibly small packages.

The third chapter will address the multiple-objective optimization problem for a global persistent coverage constellation of communications spacecraft in Low Earth Orbit. A genetic algorithm was implemented in MATLAB to explore the design space – 288 trillion possibilities – utilizing the Satellite Tool Kit (STK) software developers kit. …


Robot Arm Control Method Based On Deep Reinforcement Learning, Heyu Li, Zhilong Zhao, Gu Lei, Liqin Guo, Zeng Bi, Tingyu Lin Dec 2019

Robot Arm Control Method Based On Deep Reinforcement Learning, Heyu Li, Zhilong Zhao, Gu Lei, Liqin Guo, Zeng Bi, Tingyu Lin

Journal of System Simulation

Abstract: Deep reinforcement learning continues to explore in the environment and adjusts the neural network parameters by the reward function. The actual production line can not be used as the trial and error environment for the algorithm, so there is not enough data. For that, this paper constructs a virtual robot arm simulation environment, including the robot arm and the object. The Deep Deterministic Policy Gradient (DDPG),in which the state variables and reward function are set,is trained by deep reinforcement learning algorithm in the simulation environment to realize the target of controlling the robot arm to move the gripper below …


Multi-Agent Collaborative Exploration Through Graph-Based Deep Reinforcement Learning, Tianze Luo, Budhitama Subagdja, Ah-Hwee Tan, Ah-Hwee Tan Oct 2019

Multi-Agent Collaborative Exploration Through Graph-Based Deep Reinforcement Learning, Tianze Luo, Budhitama Subagdja, Ah-Hwee Tan, Ah-Hwee Tan

Research Collection School Of Computing and Information Systems

Autonomous exploration by a single or multiple agents in an unknown environment leads to various applications in automation, such as cleaning, search and rescue, etc. Traditional methods normally take frontier locations and segmented regions of the environment into account to efficiently allocate target locations to different agents to visit. They may employ ad hoc solutions to allocate the task to the agents, but the allocation may not be efficient. In the literature, few studies focused on enhancing the traditional methods by applying machine learning models for agent performance improvement. In this paper, we propose a graph-based deep reinforcement learning approach …


Dp-Q(Λ): Real-Time Path Planning For Multi-Agent In Large-Scale Web3d Scene, Fengting Yan, Jinyuan Jia Apr 2019

Dp-Q(Λ): Real-Time Path Planning For Multi-Agent In Large-Scale Web3d Scene, Fengting Yan, Jinyuan Jia

Journal of System Simulation

Abstract: The path planning of multi-agent in an unknown large-scale scene needs an efficient and stable algorithm, and needs to solve multi-agent collision avoidance problem, and then completes a real-time path planning in Web3D. To solve above problems, the DP-Q(λ) algorithm is proposed; and the direction constraints, high reward or punishment weight training methods are used to adjust the values of reward or punishment by using a probability p (0-1 random number). The value from reward or punishment determines its next step path planning strategy. If the next position is free, the agent could walk to it. The above strategy …


Application Of Retrograde Analysis To Fighting Games, Kristen Yu Jan 2019

Application Of Retrograde Analysis To Fighting Games, Kristen Yu

Electronic Theses and Dissertations

With the advent of the fighting game AI competition, there has been recent interest in two-player fighting games. Monte-Carlo Tree-Search approaches currently dominate the competition, but it is unclear if this is the best approach for all fighting games. In this thesis we study the design of two-player fighting games and the consequences of the game design on the types of AI that should be used for playing the game, as well as formally define the state space that fighting games are based on. Additionally, we also characterize how AI can solve the game given a simultaneous action game model, …


Regression Tree Construction For Reinforcement Learning Problems With A General Action Space, Anthony S. Bush Jr Jan 2019

Regression Tree Construction For Reinforcement Learning Problems With A General Action Space, Anthony S. Bush Jr

College of Graduate Studies: Theses & Dissertations

Part of the implementation of Reinforcement Learning is constructing a regression of values against states and actions and using that regression model to optimize over actions for a given state. One such common regression technique is that of a decision tree; or in the case of continuous input, a regression tree. In such a case, we fix the states and optimize over actions; however, standard regression trees do not easily optimize over a subset of the input variables\cite{Card1993}. The technique we propose in this thesis is a hybrid of regression trees and kernel regression. First, a regression tree splits over …